Mridang Class 1 English Worksheets Pdf Free Download

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Mridang Workbook Class 1 Unit 1 My Family and Me

Mridang Class 1 Worksheet Unit 2 Life Around Us

Mridang NCERT Book Class 1 Worksheet Unit 3 Food

Class 1 English Mridang Worksheet Unit 4 Seasons

NCERT Solutions for Class 1

Sarangi Class 1 Hindi Worksheets Pdf Free Download

NCERT Class 1 Hindi Sarangi Worksheets Pdf Free Download

Sarangi Class 1 Worksheet इकाई 1 परिवार

Class 1 Hindi Sarangi Worksheet इकाई 2 जीव-जगत

Sarangi Workbook Class 1 इकाई 3 हमारा खान-पान

Class 1 Sarangi Worksheet इकाई 4 त्योहार और मेले

Sarangi NCERT Book Class 1 Worksheet इकाई 5 हरी-भरी दुनिया

NCERT Solutions for Class 1

Joyful Mathematics Class 1 Worksheets Pdf Free Download

NCERT Class 1 Maths Joyful Mathematics Worksheets Pdf Free Download

NCERT Solutions for Class 1

Sarangi Class 2 Hindi Worksheets Pdf Free Download

NCERT Class 2 Hindi Sarangi Worksheets Pdf Free Download

Sarangi Class 2 Worksheet इकाई 1 परिवार

Class 2 Hindi Sarangi Worksheet इकाई 2 रंग ही रंग

Sarangi Workbook Class 2 इकाई 3 हरी-भरी धरती

Class 2 Sarangi Worksheet इकाई 4 मित्रता

Sarangi NCERT Book Class 2 Worksheet इकाई 5 आकाश

NCERT Solutions for Class 2

Mridang Class 2 English Worksheets Pdf Free Download

NCERT Class 2 English Mridang Worksheets Pdf Free Download

Class 2 Mridang Worksheet Unit 1 Fun with Friends

Mridang Workbook Class 2 Unit 2 Welcome to My World

Mridang Class 2 Worksheet Unit 3 Going Places

Mridang NCERT Book Class 2 Worksheet Unit 4 Life Around Us

Class 2 English Mridang Worksheet Unit 5 Harmony

NCERT Solutions for Class 2

Joyful Mathematics Class 2 Worksheets Pdf Free Download

NCERT Class 2 Maths Joyful Mathematics Worksheets Pdf Free Download

NCERT Solutions for Class 2

Area Under Curve Calculator | Free Online Calculator Tool

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.

Must Read:

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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

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

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

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 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

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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