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Area Under Curve Calculator | Free Online Calculator Tool

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Area Under Curve Calculator

Area Under Curve Calculator solves the input function and gives the output in the blink of an eye. Enter input function and range in the fields of the input section and press on the calculate button to find the area under the given curve in the fraction of seconds.

Area Under Curve Calculator: Are you searching for a tool that solves the area under the given curve? Then you are at the right place. This handy calculator tool will help you to get the accurate answer along with the step by step process easily. Get to know the process on how to find the area under curve by hand in the following sections.

How to Solve Area Under the Curve?

Area under the given function having lower and upper limits are given by the definite integration. Have a look at the below sections to get the clear step by step explanation to find the area under curve manually.

  • Let us take any function f(x) and limits x = a, x = b
  • Apply the definite integration to the function with limits upper as b and lower limit as a.
  • Calculate the integration and substitute a and b values in the result.
  • Subtract f(b) from f(a) to get the answer.

Example

Question: Find the area of the region under the curve y = x2 + 1 having x = 0 and x = 1?

Solution:

Given that,

y = x2 + 1

Area = ∫01 x2 + 1 dx

= x3/3 + x ]01

= (1/3 + 1) – (0/3 + 0)

= 1+3 / 3

= 4/3

Area = 4/3

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

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FAQs on Area Under Curve Calculator

1. What is the formula to calculate the Area Under the Curve?

The simple formula to get the area under the curve is as follows

A = ∫ab f(x) dx.

Where, a and b are the limits of the function

f(x) is the function.

2. What is the definition of area under the curve?

Area under the curve is the definite integral of a curve that describes the variation of a drug concentration in blood plasma as a function of time. It is a measure of how much drug reaches the person bloodstream in a period of time after a dose is given. This information is helpful in determining dosing and identifying potential drug interactions.

3. Why does the antiderivative of a function give you the area under the curve?

If you integrate the function f(x), then you will get the anti derivative of F(x). By evaluating the antiderivative over a specific domain [a, b] gives the area under the curve. Otherwise, perform F(b) – F(a) to find the area under f(x).

4. Calculate the area under the curve of a function, f(x) = 7 – x2, the limit is given as x = -1 to 2?

f(x) = 7 – x2 and limits x = -1 to 2

Area = ∫-12 (7 – x2) dx

= 7x – x3/3 ]-12

= (7×2 – 23 / 3) – (7(-1) – (-1)3/3)

= [(42 – 8)/3] – [(1 – 21)/3]

= (34 + 20)/3

= 54/3

Area = 18

Trapezoidal Rule Calculator | Online Free Calculator Tool

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Trapezoidal Rule Calculator

Trapezoidal Rule Calculator simply requires input function, range and number of trapezoids in the specified input fields to get the exact results within no time. So, enter your details in the below input box and click on the calculate button to get the answer in fraction of seconds.

Trapezoidal Rule Calculator: No need to feel solving any function using trapezoidal rule is a bit difficult. Our handy calculator tool gives the answer easily and quickly. Along with this free calculator, you can also get the detailed explanation to solve the integration functions using trapezoidal rule. Have a look at the example, trapezoidal rule definition and formula in the below sections.

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Steps to Solve Integration Function using Trapezoidal Rule

Follow these simple and easy guidelines to solve any function integration using trapezoidal rule manually.

  • Take any function f(x) with integration and lower, upper limits i.e a,b.
  • Also, know the number of trapezoids n.
  • The formula to compute trapezoidal rule of any function is
  • ∫ab f(x)dx ≈ Δx/2 [f(x0) + 2f(x1) + 2f(x2)+. . . +2f(xn-1) + f(xn)
  • Where, Δx = (b-a)/n.
  • Divide the given interval into n portions of length Δx.
  • In the subintervals last one is b and first one is a.
  • Evaluate the functions at those subinterval values.
  • Substitute the obtained values in the formula of trapezoidal rule and sum up the values to get the approximate value.

Example

Question: Use the Trapezoidal Rule with n = 5 to approximate ∫a=0b=1 √(1+sin3(x).

Solution:

Given that,

function f(x) = √(1+sin3(x)

a= 0, b= 1, n=5.

Trapezoidal Rule dtates that

∫ab f(x)dx ≈ Δx/2 [f(x0) + 2f(x1) + 2f(x2)+. . . +2f(xn-1) + f(xn), where

Δx = (b-a)/n

Substitute the given values in above formula to get Δx value.

Δx = 1-0/5 = 1/5

Divide the interval [0,1] into n=5 subintervals of length Δx=1/5, with the following endpoints:

a = 0, 1/5, 2/5, 3/5, 4/5, 1= b

Evaluate the function at these end points:

f(x0) = f(a) = f(0) = √(1+sin3(0) = 1

2f(x1) = 2f(1/5) = 2√(1+sin3(1/5) = 2.00782606791279

2f(x2) = 2f(2/5) = 2√(1+sin3(2/5) = 2.05820697233265

2f(x3) = 2f(3/5) = 2√(1+sin3(3/5) = 2.17257446116512

2f(x4) = 2f(4/5) = 2√(1+sin3(4/5) = 2.34021475342487

f(x5) = f(1) = 2√(1+sin3(1) = 1.26325897447473

Δx/2 = 1/10

Finally sum up the above values and multiply by Δx/2

= ⅒ (1 + 2.00782606791279 + 2.05820697233265 + 2.17257446116512 + 2.34021475342487 + 1.26325897447473)

= 1.08420812293102

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

FAQs on Trapezoidal Rule Calculator

1. What is meant by Trapezoid Rule?

Trapezoid Rule is to find the exact value of a definite integral using a numerical method. This rule is based on the Newton-Cotes formula which states that one can get the exact value of the integral as an nth order polynomial. Trapezium rule works by approximating the region under the graph of function as a trapezoid and calculating its area.

2. Where do we use Trapezoid Rule?

Trapezoid Rule is a rule that is used to determine the area under the curve. In this method, the area under the curve by dividing the total area into smaller trapezoids instead of dividing into rectangles. Integration method works by approximating the area under the graph of a function as a trapezoid and it calculates the area.

3. What is the Trapezoid Rule Formula?

Trapezoidal Rule formula is mentioned here:

∫ab f(x)dx ≈ Δx/2 [f(x0) + 2f(x1) + 2f(x2)+. . . +2f(xn-1) + f(xn),

where

Δx = (b-a)/n

4. Approximate the integral ∫01 x3 dx using the Trapezoidal Rule with n = 2 subintervals.

Trapezoidal Rule formula with n = 2 subintervals is

T = Δx/2 [f(x0) + 2f(x1) + f(x2)]

Δx = (b-a)/n

=1-0/2 = 1/2

f(x0) = f(0) = 0

f(x1) = f(1/2) = (1/2)3 = 1/8

f(x2) = f(1) = 13 = 1

So,

∫01 x3 dx ≈ 1/4 [0+ 2x(1/8) + 1] = 1/4 x 5/4 = 5/16

Second Order Differential Equation Calculator | Second ODE Calculator

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Second Order Differential Equation Calculator

Free online Second Order Differential Equation Calculator is designed to check the second order differential of the given expression and display the result within seconds. Provide your equation as the input value and hit the calculate button to get the second order derivatives along with work. Must Read: MGL Pivot Point Calculator

Second Order Differential Equation Calculator: Second order differential equation is an ordinary differential equation with the derivative function 2. Go to the below sections to know the step by step process to learn the Second Order Differential Equation with an example. The Handy Calculator tool provides you the result without delay.

Second Order Differential Equation is represented as d^2y/dx^2=f”’(x)=y’’. Have a look at the following steps and use them while solving the second order differential equation.

  • Take any equation with second order differential equation
  • Let us assume dy/dx as an variable r
  • Substitute the variable r in the given equation
  • It will form a binomial equation
  • Solve the equation and find its factors
  • Find the value of y

Example:

Question: Solve d^2y/dx^2-10dy/dx+25y=0?

Answer:

Given equation is

d2y/dx2-10dy/dx+25y=0

Let us take y=erx then

dy/dx=rerx

d2y/dx2=r2erx

Substitute these values in the equation

r2erx-10rerx+25erx=0

erx (r2-10r+25)=0

r2-10r+25=0

r2-5r-5r+25=0

r(r-5)-5(r-5)=0

(r-5)(r-5)=0

r=5

So, we can say that y=e5x

dy/dx=5e5x

d2y/dx2=25e5x

So,

d2y/dx2-10dy/dx+25y

=25e5x-10*5e5x+25e5x

=25e5x-50e5x+25e5x

=0

So, in this case our solution is

y=Ae5x+Bxe5x

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FAQs on Second Order Differential Equation Calculator

1. How many solutions does a second order differential equation have?

To construct the general solution for a second order equation, we need to take two independent solutions. So, it has 2 solutions.

2. How do you solve a second order differential equation?

Consider any variable for the derivative and substitute that value in the equation. Find the roots of that variable and substitute the values in the given equation.

3. How do you write a second order differential equation?

The standard form of a second order differential equation is pd2y/dx2+qdx/dy+r=0. The mathematical operator can be either plus or minus.

4. What is the difference between first and second order differential equations?

An equation having only first derivatives is known as a first order differential equation and an equation containing a second derivative is called a second order differential equation. First order differential equation is represented as dy/dx while the second order differential equation representation is d2y/dx2.

Parabola Calculator | Calculator to solve Parabola Equation

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Parabola Calculator

Use this user friendly Parabola Calculator tool to get the output in a short span of time. You just need to enter the parabola equation in the specified input fields and hit on the calculator button to acquire vertex, x intercept, y intercept, focus, axis of symmetry, and directrix as output.

Parabola Calculator: Are you trying to solve the parabola equation? If yes, this is the right spot for you. From here you will be going to learn the process of calculating parabola equation and finding vertex, focus, x and y intercepts, directrix and axis of symmetry values. By checking the below sections, you will get a good knowledge on the parabola equation concept and you will also obtain a handy calculator tool that gives result in fraction of seconds.

How to Solve the Parabola Equation?

We can find the x intercept, y intercept, vertex, focus, directrix, axis of symmetry using any parabola equation in the form of y = ax2 + bx + c. In the following sections, we are providing the simple steps to find all those parameters of parabola equation. Follow them while solving the equation.

  • At first, take any parabola equation.
  • Find out a, b, c values in the given equation
  • Substitute those values in the below formulae
  • Vertex v (h, k).
  • h = -b / (2a), k = c – b2 / (4a).
  • Focus of the x coordinate is -b/2a.
  • Focus of the y coordinate is c – (b2 – 1)/ (4a)
  • Then, focus is (x, y)
  • Directrix equation y = c – (b2 + 1) / (4a)
  • Axis of symmetry is -b/ 2a.
  • Solve the y intercept by keeping x = 0 in the parabola equation.
  • Perform all mathematical operations to get the required values.

Examples

Question 1: Find vertex, focus, y-intercept, x-intercept, directrix, and axis of symmetry for the parabola equation y = 5x2 + 4x + 10?

Solution:

Given Parabola equation is y = 5x2 + 4x + 10

The standard form of the equation is y = ax2 + bx + c

So, a = 5, b = 4, c = 10

The parabola equation in vertex form is y = a(x-h)2 + k

h = -b / (2a) = -4 / (2.5)

= -2/5

k = c – b2 / (4a)

= 10 – 42 / (4.5)

= 10- 16 / 20 = 10*20 – 16 / 20

= 184/ 20 = 46/5

y = 5(x-(-2/5))2 + 46/5

= 5(x+2/5)2 + 46/5

Vertex is (-2/5, 46/5)

The focus of x coordinate = -b/ 2a = -2/5

Focus of y coordinate is = c – (b2 – 1)/ (4a)

= 10 – (16 – 1) / (4.5)

= 10 – 15/20

= 37/4

Focus is (-2/5, 37/4)

Directrix equation y = c – (b2 + 1) / (4a)

= 10 – (42 + 1) / (4.5)

= 10 – 17 / 20

=200 – 17 / 20

=183/20

Axis of Symmetry = -b/ 2a = -2/5

To get y-intercept put x = 0 in the equation

y = 5(0)2 + 4(0) + 10

y = 10

To get x-intercept put y = 0 in the equation

0 = 5x2 + 4x + 10

No x-intercept.

Question 2: Find the equation, focus, axis of symmetry, vertex, directrix, focal parameter, x-intercepts, y-intercepts of the parabola that passes through the points (1,4), (2,9), (−1,6)?

Solution:

Given points are (1,4), (2,9), (−1,6)

The standard form of the equation of the parabola is y = ax2 + bx + c

When the parabola passes through the point (1,4) then, 4 = a+b+c

when the parabola passes through the point (2,9), then 9 = a(2)2 + b(2) + c = 4a + 2b + c

when the parabola passes through the point (-1,6), then 6 = a – b + c

Solve first and third equation

a + b+ c = 4

a – b + c = 6

2(a + c) = 10

a + c = 10/2 = 5

substitute a + c = 5 in first equation

5 + b = 4

b = 4-5

b = -1

Put a = 5-c, b = -1 in second equation

4(5- c) -2 + c = 9

20 – 4c -2 +c = 9

18 – 3c = 9

18-9 = 3c

c = 3

Substitute b = -1 c = 3 in the third equation

a +1 + 3 = 6

a + 4 = 6

a = 2

Put a =2, b = -1, c = 3 in the standard form of parabola equation

y = 2x2 – x + 3

The parabola equation in vertex form is y = a(x-h)2 + k

h = -b / (2a) = 1/4

k = c – b2 / (4a) = 3 – 1 / 8 = 23/8

y = 2(x-1/4)2 + 23/8

Vertex is (1/4, 23/8)

The focus of x coordinate = -b/ 2a = 1/4

Focus of y coordinate is = c – (b2 – 1)/ (4a)

= 3 – (1 – 1) / (4.2)

= 3/8

Focus is (1/4, 3/8)

Directrix equation y = c – (b2 + 1) / (4a)

= 3 – (1 + 1) / (4.2)

= 3-2/8

=24-2/8 = 22/8 = 11/4

Axis of Symmetry = -b/ 2a = 1/4

To get y-intercept put x = 0 in the equation

y = 2(0)2 – 0 + 3

y = 3

y intercept (0, 3)

To get x-intercept put y = 0 in the equation

0 = 2x2 – x + 3

No x-intercept.

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

FAQs on Parabola Calculator

1. What is meant by parabola?

Parabola is a curve where any point is at an equal distance from a fixed point (focus) and a fixed straight line (directrix).

2. Where is parabola used in real life?

Parabola can be seen in nature or in man made items. From the paths of thrown baseballs, to fountains, even functions, to satellite, and radio waves.

3. Where is the focus of a parabola?

A parabola is set of all points in a plane which are equal distance from a given point and given line. The point is called parabola focus and the line is known as directrix of parabola. The focus lies on the axis of symmetry of the parabola.

4. What is a parabola used for?

The parabola has many important applications, from a parabolic microphone or parabolic antenna to automobile headlight reflectors and the design of ballistic missiles. They are frequently used in engineering, physics and other areas.

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Radius of Convergence Calculator | Online Calculator Tool

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Radius of Convergence Calculator

Free online Radius of Convergence Calculator tool evaluates the radius of a convergence of a power series. Simply enter your function and variable range in the given input sections and tap on the calculate button to get the instant output along with a detailed procedure.

Radius of Convergence Calculator: If you want to know the radius of convergence of a power series equation and need any help? Then we are here you to assist for any kind of math solutions. Have a look at the Radius of Convergence Calculator to solve the power series function within seconds. This article gives a detailed description of steps to solve the radius of convergence manually and we will explain it with few examples.

Method to Calculate Radius of Convergence of a Power Series

Follow these simple steps to find out the radius of convergence of a power series

  • Take a power series
  • Consider the value of x for which the power series will converge
  • To get the radius of convergence, find out ratio test
  • And evaluate the function as per the ratio test
  • Ratio test will gives you the limit value
  • Substitute the limit value to get the R i.e Radius of Convergence

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

Example

Question: Find the Radius of Convergence for the power series Sigma n=to infinity 2n/nx(4x-8)n

Solution:

Let us take Cn=2n/nx(4x-8)n

We know that this power series will converge for x=2

For the above power series, the ratio test will be

L=Cn+1/Cn

L=lim n to infinity 2n+1(4x-8)n+1/n+1*n/2n(4x-8)n

lim n to infinity 2n(4x-8)/n+1

(4x-8) lim n to infinity 2n/n+1

=2(4x-8)

So we will get the below convergence info from this

2(4x-8)<1

x-aR

8(x-2)<1

(x-2)<⅛

8(x-2)>1

(x-2)>1/8

So, the radius of convergence for the power series is R=1/8

FAQs on Radius of Convegence

1. What is the Radius of Convergence?

Radius of Convergence of a power series is the radius of the largest disk in which the series converges. It will be non negative real number or infinity. In the positive case, the power series converges absolutely.

2. What is the radius of convergence is 0?

The radius of convergence R =0 tells that the distance between the center of a power series interval of convergence and its endpoints.

3. Can the radius of convergence be negative?

No, the radius of convergence can never be a negative number.

4. What is the ratio test for convergence?

The ratio test defines that: if L<1 then the series is convergent or if L>1 then the series is divergent. In case L=1, tes is inclusive, because it satisfies both convergent and divergent.

ATUL Pivot Point Calculator

Laplace Transform Calculator | Quick & Easy Process

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Laplace Transform Calculator

Laplace Transform Calculator: If you are interested in knowing the concept to find the Laplace Transform of a function, then stay on this page. Here, you can see the easy and simple step by step procedure for calculating the laplace transform.

This Laplace Transform Calculator handy tool is easy to use and shows the steps so that you can learn the topic easily. We are providing the best examples so that you can understand the concept. Make your calculations faster with the help of our free online tool.

Solve Laplace Transform of a Function

We all know that calculating Laplace Transform is a little bit tough when compared with other mathematical operations. Have a look at the detailed step by step procedure that is helpful in solving the Laplace Transform of any kind of equation.

  • Take a fiction or an equation to which you want to perform the operation.
  • Perform the integration operation on the given function.
  • Do all mathematical calculations to the solution.
  • Substitute the values in the obtained equation to get the result.

Standard Form

The standard form to represent the Laplace Transform is

F(s)=L(f(x))= Integration 0 to infinity e^-stf(t)dt

where f(t) is a function

s is the complex number frequency parameter

Example:

Question: What is the Laplace Transform of 3sinh(2t)+3sin(2t)?

Solution:

Let us take the functions f(t), g(t)

f(t)=sinh(2t)

g(t)=sin(2t)

Use the linearity property of Laplace Transform

L[a.f(t)+b.g(t)]=a.L[f(t)]+b.L[g(t)]

L[sinh(2t)]=2/s2-4

Lsin(2t)]=2/s2+4

L[3sinh(2t)+3sin(2t)]=3×2/s2-4+3×2/s2+4

=6/s2-4+6/s2+4=6x{1/s2-4+1/s2+4}

=6x{s2+4+s2-4/s4-16}

=6x{2s2/s4-16}

=12s2/s4-16

The Laplace Transform of 3sinh(2t)+3sin(2t) is 12s2/s4-16.

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

Frequently Asked Questions on Laplace Transforms

1. What is the purpose of Laplace Transform?

The purpose of the Laplace Transform is to transform ordinary differential equations into algebraic equations. Like the Fourier transform, it is used for solving the integral equations.

2. What are the applications of the Laplace Transform?

The applications of Laplace Transform are Circuit Analysis, Signal Processing, and Communication Systems.

3. Is Laplace Transform linear?

Yes, Laplace Transform is linear.

4. What is the difference between Laplace and Fourier Transform?

The fourier transform doesn’t care about changing the magnitudes of a signal. But the laplace transform cares both changing magnitudes and oscillation parts. Actually, the Fourier Transform is a subset of the Laplace Transform.

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Convert CGPA to Percentage | How to Calculate CGPA from Percentage?

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Convert CGPA to Percentage

Convert CGPA to Percentage: Every year, the count of students increases appearing for CBSE exams. However, they have much stress in their minds as rewarding marks changes after some years. Thus students need to be very careful in every aspect. However, the system of CGPA calculation confuses them a bit. The feeling is quite different when they think of the final CGPA for their preparation.

However, this system of CGPA put minds to think about calculating the final percentage in every subject. Results are even more important if you are planning to study abroad. International universities demand high previous class scores and standard test results. Most of them also raise the demand for good CGPA. However, the term seems to be quite confusing. But we have tried to resolve it through the blog below. Below you will understand the important aspects while converting CGPA into a percentage.

How Can You Convert CGPA to Percentage?

According to the Central Board of Secondary Education’s terms and conditions, you need to multiply CGPA by 9.5 to get your percentage. Let us consider an example. Suppose your CGPA is 9.4, then multiply it with 9.5, and the resultant 89.3 is our percentage.

What does CGPA Actually Define?

CGPA is a Cumulative Grade Point Average. Before you start converting your CGPA into a percentage, it is imperative to define CGPA. Usually, we see CGPA results on our 10th result card. We define CGPA as the average of the collective grade points that we score in the subjects in a year. The grading system is supported by CBSE, which is allotted based on a range of marks. Take an example of grade A. It is allotted to the students obtaining marks between 90-95. Thus their grade point will be 9.

Now, if you have your grade points, how will you calculate CGPA with it? Take the example of a total of 5 subjects. You have grade points of each, and CGPA is the average of all. Sum your grade points and divide by 5. This is how you obtain CGPA. Similarly, if you want to find a percentage in each subject, multiply each grade point by 9.5.

CGPA to Percentage

Which is the Right Formula to Convert CGPA to Percentage?

The basic formula of calculating CGPA is through grade points scored in each subject which is further calculated based on a range of marks. Get the grade points of all, add them and divide by a total number of subjects. This is how you calculate your CGPA. Further, to calculate the percentage, multiply your CGPA by 9.5, and the resultant is your percentage.

Some Important Examples of Calculating CGPA to Percentage

Example 1

Calculate the CGPA if you have 9 in Science, 7 in English, 9 in Hindi, 8 in Social Science, and 10 in Mathematics. Also, calculate the overall percentage and percentage in each subject.

There are a total of 5 subjects for your class as per the question.

Total grade points earned= 9 + 7 + 9 + 8 + 10 = 43.

CGPA= 43/ 5 = 8.6.

Total percentage= 8.6 x 9.5 = 81.7%

Percentage in each subject:

Name of the Subject CGPA Percentage
Science 9 85.5
Maths 10 95
English 7 66.5
Social Science 8 76
Hindi 9 85.5

CBSE Conversion Certificate

CBSE students are well aware of the marking scheme of the 10th and 12th standards. It is according to the grade points earned in each subject, and the average grade point referred to as CGPA. According to CBSE, grade points are assigned as A1, A2, B1, B2…..

While you are into your exam, you will get a certificate that clearly mentions grade points with the corresponding marks range.

For Example

If your grade point is 10, that means your grade is A1 and marks are between 91-100.

What is the Reason for Multiplying 9.5?

Assigning grade systems and CGPA systems is not an everyday task. CBSE that undergone a complete survey for the same. They took a record of students from the past five years and found that the average marks of the students who have earned a band between 91-100 are 95. This is grade A1 with a grade point of 10. Now, after dividing the average marks by 10, we get 9.5. This is how CBSE used the 9.5 factor to calculate the percentage.

How to Get CGPA from Percentage for Engineering?

Now suppose you are given the percentage of marks obtained. What will be the CGPA earned? To calculate CGPA from percentage, reverse the use of 9.5. Divide 9.5 by percent of marks obtained by you. Suppose your percentage is 94%, then CGPA is 94/ 9.5. The resultant 9.8 is your CGPA.

CGPA to Percentage in Terms of UPSC

The percentage from CGPA is calculated according to its own terms. One such example is CBSE. However, if you submit your final percent obtained if the university asks for the same, you need to submit according to their guidelines. In case you don’t know the calculation system, UPSC has given an overall formula to calculate the percentage. Suppose your undergraduate level CGPA is 9.0, and your university asks you to submit your percentage, then multiply it with 10 to get your percentage. Your percentage will be 90.

What are the Benefits of the CGPA system?

  • CGPA is basically a grade point system. These grade points help in developing good competition among students. The fact is, none obtains specific marks or ranks in their finals. Thus it helps in the good development of the student’s academic mind.
  • Your percentage, according to the CGPA system, will define aggregate marks. CGPA defines your marks in the form of grades.
  • It is easy to work with CGPA, while on the other hand, it is good to go with a percentage. Both the systems are important to understand in every aspect.
  • Some universities consider both the system. Thus, you need to be sure and clarify your doubts, if any, with CGPA and the percentage system. Various universities provide a formula to calculate percentage from CGPA as per their guidelines. If not so, you can multiply it by 10. This is universally accepted.

Also, Read:

How CGPA Differs from Percentage?

The below table clearly defines how the percentage varies from CGPA:

CGPA Percentage
It is calculated with the average of grade points earned. It is calculated with the average of actual marks obtained.
CBSE and other universities use this system Used by various educational institutions
Promotes healthy academic mind among students Bring challenges among students.
Best performance of the candidates throughout the year. An easy and simple system
It is effortless to get a percentage from CGPA. It needs a lot of calculations while calculating the actual percentage.

CGPA to Percentage in Terms of CBSE

The below table mentions CGPA with the corresponding percentage earned by the students according to CBSE.

CGPA Percentage
10 95
9.8 93.1
9.6 91.2
9.4 89.3
9.2 87.4
9.0 85.5
8.8 83.6
8.6 81.7
8.4 79.8
8.2 77.9
8.0 76
7.8 74.1
7.6 72.2
7.4 70.3
7.2 68.4
7.0 66.5

CGPA Benefits

How GPA Differs from CGPA?

The grading system is not only limited to CGPA but also about GPA. CGPA is a term used in India, but GPA is recognized in the entire world. GPA is actually the grade points obtained every semester. CGPA is actually the average of all credits earned, marks obtained, and grades obtained. However, if you plan for an abroad study, you need to submit your points according to the universally accepted method. Be prepared to mention your grades in a professional tone. However, if you target any university, you need to understand their calculating policy and mentioned grades accordingly.

Grade Table According to CBSE

It is not the only CGPA mentioned in your final report and additional grades and grade points. You can convert your grade to the corresponding number. The below will help you out:

Marks Grade Grade Points
91-100 A1 10
81-90 A2 9
71-80 B1 8
61-70 B2 7
51-60 C1 6
41-50 C2 5
33-40 D 4
21-32 E1
0-20 E2

The 10 Point Scale

The 10 point Scale is considered the highest marks obtained by a student. Suppose the highest marks obtained are 94, then 94 will be 100%. If a student gets 85 marks in a particular subject, then CGPA is calculated concerning [100/94] / 85 = 85.10. Hence the CGPA will be 8.5 according to the 10 point scale.

CGPA to Percentage According to Indian Universities

Universities want to keep records of the percentage of marks obtained. However, the calculation is different according to their guidelines. Hence students need to refer to their official websites for the same. Here are a few examples from the top universities of India.

CGPA to Percentage According to DU

Delhi University released its Percentage calculation scheme on 11 January 2018. According to the marking scheme:

Percentage = 9.5 x CGPA of all semester

Convert CGPA To Percentage Mumbai University Calculator

Mumbai University has also recently released its Percentage calculation scheme in 2018. It specifies a different scheme for varied programs. 7 point scale is used in arts, pure science, commerce, and related programs. For engineering, 10 point grade scale is used.

Percentage= 7.25 * CGPA +11

Convert CGPA To Percentage Anna University

CGPA to % conversion is also declared by Anna University in 2018. However, the scheme keeps changing for many years.

Convert CGPA To Percentage GTU

Gujarat Technological University also declares its method of calculating % from CGPA.

Percentage: [(CGPA/SPI/CPI-0.5)] *10

CGPA to Percentage According to APJ Abdul Kalam Technological University

KTU has simplified its way of calculating CGPA. According to them,

CGPA= Sum of (Ci*GPi)/ Sum of (Ci)

Convert CGPA to Percentage VTU

For students aspiring to get admitted to VTU, the percentage calculation is different from other standards used to date. According to them,

Percentage = [CGPA-0.75] * 10

FAQ’s on Converting CGPA to Percentage

Question 1.
Define CGPA after learning different aspects.

Answer:
CGPA is the average obtained by the students out of 10. It is a highly preferred marking scheme for the 10th standard.

Question 2.
How CBSE defines calculating CGPA?

Answer:
According to CBSE, CGPA is the average of grade points scored in each subject. Suppose we have five subjects in total. Then

CGPA = Total grade points earned / total number of subjects.

Question 3.
What are other additional subjects other than the five main subjects declared on the mark sheet?

Answer:
Class 10th deals with a total of 6 subjects. Five are compulsory, and one it optional to choose as per wish. However, CBSE calculates CGPA on the five main subjects.

Question 4.
What is the percentage of 8.6 CGPA according to CBSE?

Answer:
Multiply the CGPA obtained with 9.5 according to CBSE guidelines. Hence % earned is 81.7%.

Boolean Algebra Calculator | Online Tool to solve Boolean Expression

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Boolean Algebra Calculator

With the help of our handy Boolean Algebra Calculator tool, you can easily solve any difficult boolean algebraic expression in seconds. Provide your boolean expression as the input and press the calculate button to get the result as early as possible.

Boolean Algebra Calculator: Evaluating the boolean algebraic expressions is not like solving any other mathematical expressions. It is possible by taking the help of various boolean laws and proper knowledge on them. Without all these, you can simply solve your equation by using our free online boolean algebra calculator tool. From this article, you can find the detailed procedure for computing your questions.

How to Solve Boolean Algebra Expression?

In the following sections you can get the step by step process to solve a boolean expression. Go through the below segments and follow them. Two simple steps to solve the boolean expression is by doing the truth table for each operation and finding the result. Another easy step is right here.

  • Take any boolean expression
  • Know all the Laws of Boolean Algebra
  • Replace the Boolean Algebra Laws at each possible step with proper knowledge
  • Keep on doing the step 3 till you reach a point where you can’t substitute any law
  • The resultant will be your answer with no doubt

Laws of Boolean Algebra

Here, we are providing the basic laws of boolean algebra that assist you when solving the boolean algebra expression.

    • Idempotent Law

A * A = A

A + A = A

    • Associative Law

(A * B) * C = A * (B * C)

(A + B) + C = A + (B + C)

    • Commutative Law

A * B = B * A

A + B = B + A

    • Distributive Law

A * (B + C) = A * B + A * C

A + (B * C) = (A + B) * (A + C)

    • Identity Law

A * 0 = 0 and A * 1 = A

A + 1 = 1 and A + 0 = A

    • Complement Law

A * ~A = 0

A + ~A = 1

    • Involution Law

~(~A) = A

    • DeMorgan’s Law

~(A * B) = ~A + ~B

~(A + B) = ~A * ~B

    • Redundancy Laws

Absorption

A + (A * B) = A

A * (A + B) = A

(A * B) + (A * ~B) = A

(A + B) * (A + ~B) = A

A + (~A * B) = A + B

A * (~A + B) = A * B

Example:

Question: Solve ~(A * B) * (~A + B) * (~B + B)?

Solution:

Given expression is ~(A * B) * (~A + B) * (~B + B)

By applying Complement law i.e ~B + B=1

=~(A * B) * (~A + B) * 1

Apply Identity law i.e (~A + B) * 1=~A + B

=~(A * B) * (~A + B)

Apply DeMorgan’s law i.e ~(A * B)=(~A + ~B)

=(~A + ~B) * (~A + B)

Distributive Law is ~A + B=B

=(~A + ~B) * B

Complement law says ~B * B=0

=~A + 0

Apply Identity law

=~A

~(A * B) * (~A + B) * (~B + B)=~A

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

Frequently Asked Questions on Boolean Algebra

1. What is meant by Boolean Algebra?

Boolean algebra is a branch of mathematics that deals with the operations on logical values. It returns only two values i.e true or false or represented by 0 and 1.

2. What are the operations used in the boolean algebra?

The various basic operations used in the boolean algebra are Conjunction (AND), Disjunction(OR), and Negotiation (NOT).

3. How do you calculate the Boolean Algebra Expression using a calculator?

Enter a valid boolean expression and hit on the calculate button to get your answer quickly.

4. What are the 7 logic gates?

There are seven basic logic gates. They are AND, OR, XOR, NOT, NAND, and XNOR.

5. What is the other name of Boolean Algebra?

Boolean Algebra is used to simplify and analyze the digital (logic) circuits. It has only the binary numbers i.e. 0 (False) and 1(True). It is also called Binary Algebra or logical Algebra.

Area Between Two Curves Calculator

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Area Between Two Curves Calculator

Online Area Between Two Curves Calculator helps you to evaluate the equations and give the exact area between two curves in a short span of time. Simply provide the two equations in the input field of the tool and click on the calculate button to check the accurate output in just seconds.

Area Between Two Curves Calculator: Students who are looking for the easiest way to find the area between two curves can make use of this handy calculator tool. Apart from the tool, you will also get the learning stuff like step by step process to find the area between two curves in detail with solved example. So, check the below sections, to get a good knowledge on the area between two curves topic and get your answers effortlessly.

Steps to find Area Between Two Curves

Follow the simple guidelines to find the area between two curves and they are along the lines

  • If we have two curves P: y = f(x), Q: y = g(x)
  • Get the intersection points of the curve by substituting one equation values in another one and make that equation has only one variable.
  • Solve that equation and find the points of intersection.
  • Draw a graph for the given curves and point of intersection.
  • Then area will be A = ∫x2x1 [f(x)-g(x)]dx
  • Substitute the values in the above formula.
  • Solve the integration and replace the values to get the result.

Example

Question: Calculate the area of the region bounded by the curves y2 + 4x – y = 0 and the straight line y = x?

Solution:

Given equations are y2 + 4x – y = 0, y=x

y2 + 4x – y = 0

Add y and subtract y2 on both sides.

y2 + 4x – y + y – y2 = y – y2

4x = y – y2

Divide by 4 on both sides

x = y – y2/4

Using another equation y = x in the equation of the curve will be

y2+4y-y = 0

y2+3y = 0

y(y+3) = 0

y = 0 or -3

Corresponding to the values of y, we get x = 0 or -3. Thus the points of intersection are P(-3,-3) and Q(0,0).

The graph for the system will be:

Area Between Two Curves

From the graph, the curve on the right is f(y) and the curve on the left is g(y).

f(y) = y – y2/4

g(y) = y

The area is A = ∫x2x1 [f(x)-g(x)]dx

A = ∫30 [(y – y2/4)-y]dy

= ∫30 ((-y2-3y)/4)dy

= [ – y3/4*3 – 3/4 * y2/2]30

= – [(0+0) – (- 33/4*3 – 3/4 * 32/2)

= – ( -27/12 + 3/4 * 9/2)

= 27/24

Area as specified by the definite integral is -27/24.

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

FAQs on Area Between Two Curves Calculator

1. What is the area between two curves?

The area between two curves is calculated by computing the difference between the definite integrals between two functions. In a two dimensional geometry, the area is a quantity that expresses the region occupied by the equations.

2. What is meant by the polar curve?

A polar curve represents a shape whose construction takes place by using the polar coordinate system. They are marked by points that exist a variable distance from the origin or pole.

3. What is the area under the curve?

The area under a curve is present between two points and can be calculated by conducting a definite integral between those two points. To find the area under the curve y = f(x) between x = a and x=b, you must integrate y = f(x) between the limits of a &b.

4. Find out the area of the region enclosed by y = sin x, y = cos x, x = π/2, and the y-axis?

From the given equations

sin x = cos x

At this interval, x = π/4.

The area will be,

A = ∫0π/4 cos x – sin x dx + ∫π/4π/2 sin x – cos x dx

= [sin x + cos x]0π/4 + [-cos x – sin x]π/4π/2

= (sin (π/4) + cos (π/4)) – (sin 0 + cos 0) + (-cos (π/2) – sin (π/2)) – (-cos (π/4) – sin (π/4))

= (√2/2 + √2/2) – (0+1) – (0+1) + (√2/2 + √2/2)

=2√2-2 = 0.828427.

5. Is it possible for the area between two curves to be negative?

No, the area between two curves will never be negative. Because, the area between two curves is not like the area under the curve. Hence, the area between the two curves is always positive.

SGPA to CGPA Conversion Formula, Examples | How to Calculate CGPA from SGPA?

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Convert SGPA to CGPA

Marks Calculation is quite an important aspect in college and school life. However, there are several methods to perform the same task of which GPA is the prominent one. Among all these methods one that appears confusing is the conversion from SGPA to CGPA. Though, SGPA and CGPA serve a similar purpose they are calculated differently. Know about the basic difference between SGPA and CGPA, Conversion Formula, Procedure on how to calculate CGPA from SGPA.

SGPA, CGPA, GPA – Definitions

Here, we will find the basic definitions of both SGPA, CGPA. Refer to them and use them during your Marks Calculations as per your requirement.

What is SGPA?

SGPA is known as Sessional Grade Point Average/Semester End Grade Point Average. It is the grade point average we calculate after the end of an academic session such as the year in school or for a semester in college. Let us add Grade Points of all Subjects in an Academic Year and their Average calculated is known as SGPA for that particular year or session.

What is CGPA?

CGPA is abbreviated as Cumulative Grade Point Average. The major difference between CGPA and SGPA is that CGPA is calculated considering the SGPA’s of different semesters in an academic year.

What is GPA?

GPA in simple terms is referred to as Grade Point Average i.e. the average given to a student throughout a semester. It can also be found depending on the different courses students have opted for. We can say that GPA indicates the achievement level of a student so that teachers can assess their performance for a particular period of time.

In Indian Grading System we use a 10 Point GPA Scale and the GPA can be calculated from percentage using the below formula

GPA = Percentage/9.5

In the US GPA Scale of 4.0 is used and to find the GPA simply divide the Percentage by 100 and then multiply with 4.

GPA = (Percentage/100)*4

How to Calculate CGPA from SGPA?

From the definitions of SGPA and CGPA, we can frame CGPA as the collection of SGPA’s calculated at the end of the year. Before, calculating the CGPA you just need to find the average of all subjects in each of the semesters i.e. SGPA. After that, add the SGPA’s of all the Semesters and divide by the number of semesters to obtain the CGPA.

CGPA= (SGPAs of All Semesters in an Academic Year)/Number of Semesters

Example:

If a student scored 6 and 8 SGPA in their two semesters, their CGPA would be

Formula to Calculate CGPA = SGPAs of All Semesters in an Academic Year/Number of Semesters

= (SGPA in Semester 1+ SGPA in Semester 2)/Number of Semesters

= (6+8)/2

= 7

Therefore CGPA is 7.

Do Read Similar Articles:

How to Convert SGPA to Percentage?

Now that you are aware of the formula for converting SGPA to CGPA let us learn how to calculate Percentage using such formulas

[(SGPA * 10) – 7.5 = Percentage]

Example:

Calculate Percentage if SGPA’s are given for 4 Semesters i.e. 7.0, 6.0, 7.2, 6.6

Total SGPA for all Semesters = (7.0+6.0+7.2+6.6)/4

= 26.8/4

= 6.7

We know the formula to calculate Percentage from SGPA is

 [(SGPA * 10) – 7.5 = Percentage]

= (6.7*10) -7.5

= 67-7.5

= 59.5%

SGPA to CGPA Calculation for KTU

Esteemed KTU (APJ Abdul Kalam Technology University) Calculates the Cumulative Grade Point Average using the Semester Grade Point Average as follows

SGPA = Σ(Ci×GPi)/ΣCi

Where Ci is the Credit assigned for a course
GPi is the Grade point for that course

SGPA to CGPA Conversion According to SPPU

Savitribai Phule Pune University determines the CGPA if the SGPA is known as such. Know the formula to Convert SGPA to CGPA by referring to the below modules.

SGPA = (C1G1 + C2G2 + C3G4 + C4G4 + C5G5)/ (C1 + C2 +C3 + C4 + C5)

Where C1, C2, C3, C4, C5 are the Course Credits
G12, G2, G3, G4, G5 are the Grade Points of the Course

SGPA to CGPA Calculation According to VTU

Visvesvaraya Technological University (VTU) uses the following formula to calculate SGPA for potential students. They are as such

SGPA = Σ(Ci×Gi)/ΣCi

Where Ci is the Credit assigned for a course
Gi is the Grade point for that course

SGPA to CGPA to Percentage

Now that you are familiar with how to calculate SGPA let us understand how to convert to CGPA. Most of the Institutes release their Scores in CGPA and while applying for abroad universities you might need to convert these scores into Percentages. Keeping your necessity in mind we have presented the Procedure on How to Calculate Percentage from CGPA. The Formula is quite simple firstly we have to convert from SGPA to CGPA and then take the total CGPA and multiply with 9.5 to get the Percentage.

Percentage = CGPA*9.5

Example:

Calculate the Percentage if CGPA is 8?

Given CGPA = 8

Formula to find the Percentage = CGPA *9.5

= 8*9.5

= 76%

8 CGPA in Percentage is 76%

SGPA Vs CGPA Vs GPA

Go through the below pointers to know the key differences between SGPA, CGPA, and GPA. They are along the lines

  • CGPA is the Cumulative GPA and is obtained by dividing Sum of SGPA’s in all the Semesters by the Number. of Semesters. In Other Words, we can say that CGPA is found for the entire course whereas GPA is for a Semester and SGPA is for a particular session such as a year or so.
  • Grading System differs from college to college. Some of them use GPA while others use CGPA to determine the scholastic abilities of a Student.
  • CGPA and GPA highlights the student’s academic performance for a stipulated period of time. The majority of the institutions prefer GPA over CGPA to provide Admissions to Candidates.
  • CGPA reflects your performance for an entire course so it is a higher one in comparison to GPA and SGPA. One more Prominent Difference is SGPA and CGPA differ on a scale of 0.0 -10.0

How to Calculate SGPA?

After learning the definition of SGPA the next essential step is to learn how to calculate SGPA. Semester Grade Point Average reflects a student’s performance for a stipulated period of time i.e. a semester or so. In order to find out SGPA, you need to consider all the credit points you have obtained in a semester and then divide them with the total number of credit points for that semester. Follow the below steps to learn how to find the SGPA.

  • In the Initial Step Multiply the Credit Point of Each Subject with the Grade Point you have obtained in the Particular Subject.
  • After that Add all the Total Grade Points you have got.
  • Now, divide the sum with the total credit points of the semester to obtain the SGPA.

Example:

Let’s say you have three subjects in a semester, and you have scored the following grade points,

Subject 1: 7; Subject 2: 6 and Subject 3: 7

Now, suppose the credit points for these subjects are:

Subject 1: 4; Subject 2: 4; Subject 3: 2

Solution:

Firstly, multiply the grade points with respective credits

Subject 1 = 7*4 = 28

Subject 2 = 6*4 = 24

Subject 3 = 7*2 = 14

Add all the Grade Points as well as the Credit Points

Grade Points = 28+24+14

= 66

Credit Points = 4+4+2

= 10

To obtain the SGPA simply divide the sum of grade points by the number of credit points

= 66/10

= 6.6

FAQs on SGPA to CGPA

1. Is SGPA and CGPA Same?

No, SGPA and CGPA aren’t the same. SGPA is the Grade Point received for a particular semester whereas CGPA is calculated for the overall Grade Point of a Year.

2. How to Calculate Percentage from CGPA?

You can calculate Percentage from CGPA using the Formula Percentage = CGPA*9.5

3. How is CGPA Calculated from SGPA?

To find the CGPA add the SGPA’s of all the semesters with the number of semesters. The result obtained is the CGPA.