Inverse Function Calculator | How to Find the Inverse of a Function?

 

Inverse function calculator helps in computing the inverse value of any function that is given as input. To recall, an inverse function is a function which can reverse another function. It is also called an anti function. It is denoted as:

f(x) = y ⇔ f− 1(y) = x

How to Use the Inverse Function Calculator?

This calculator to find inverse function is an extremely easy online tool to use. Follow the below steps to find the inverse of any function.

  • Step 1: Enter any function in the input box i.e. across “The inverse function of” text.
  • Step 2: Click on “Submit” button at the bottom of the calculator.
  • Step 3: A separate window will open where the inverse of the given function will be computed.

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.

How to Find the Inverse of a Function?

To find the inverse of any function, first, replace the function variable with the other variable and then solve for the other variable by replacing each other. An example is provided below for better understanding.

Example: Find the inverse of f(x) = y = 3x − 2

Solution:

First, replace f(x) with f(y).

Now, the equation y = 3x − 2 will become,

x = 3y − 2

Solve for y,

y = (x + 2)/3

Thus, the inverse of y = 3x − 2 is y = (x + 2)/3/

Frequently Asked Questions on Inverse Function

How do you find the inverse of a function?

To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

What is the inverse of 6?

The inverse of 6 is ⅙. For any function “x”, the inverse will be “1/x”.

Domain and Range Calculator | Best Online Calculator

Domain and Range Calculator

Use this handy Domain and Range Calculator to get the exact answer for your function instantly. All you need to do is enter the function in the input box and press the calculate button which is in blue colour to display the domain and range values of that particular function in seconds.

Domain and Range Calculator: Struggling to find the domain and range of any function. Then you can avail the handy tool Domain and Range Calculator to get the output instantaneously. In the below section, you can check the steps to solve the domain and range for square root function and polynomial function, and others. For your better understanding, we are also giving the example questions.

Steps to get the Domain and Range for Square Root or other Functions

You can observe the simple steps through which we can know the domain and range of any real valued function. Use these steps, when you are searching for a detailed process to solve the domain & range.

  • Take any real valued function
  • Find any real number for x get a meaningful output
  • Domain is all the real numbers, except for which number we are not getting the meaningful output.
  • Do the inverse function by interchanging the x and y values
  • Again, get the real numbers for which we are getting a meaningful output
  • Range is also all the real numbers except those set of numbers for which you are not getting the output.

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How to Find the Domain & Range for Real Valued Function?

  • Take any real valued linear function
  • We know that real functions are the lines that continue forever in each direction
  • Check that by substituting the any real number in the function, gives an output or not
  • Then all the real numbers are domain and range

Example

 

Question1: Find the domain and range of the function y=x2-3x-4/x+1

 

Solution

Given function is y=x2-3x-4/x+1

We can say that the function is not defined at x=-1

Because when we substitute -1for x, we get zero in the denominator

So, the domain is all real numbers except -1

Find the factors of numerator

y=(x+1)(x-4)/(x+1)

y=x-4

Substitute the x=-1 in the above equation

y=-1-4

y=-5

This means, the function is not defined when y=-5 and x=-1

Therefore the range of the function is {y belongs to R | y=!-5} and domain is {y belongs to R | x=!-1}

Question2:
What are the domain and range of the function f(x)=-2+sqrt(x+5)?

 

Answer:

Given function f(x)=-2+sqrt(x+5)

This is a radical function

Square root must be always positive or zero

sqrt(x+5)>=0, then -2+sqrt(x+5)>=-2

range is all real numbers such that f(x)>=-2

The domain of the radical equation is any x value for which the sign is not negative.

That means, x+5>=0

x>=-5

FAQs on Domain and Range

1. What is the domain and range?

Domain is a set of all values for which the function is mathematically defined. The range is the set of all possible output values (commonly the variable y or f(x)), which result from using a particular function.


2. Does every function have a domain?

Yes, every function has a domain.


3. What is the difference between domain and range?

Domain is all the values that go into function and range is all values that come out.


4. How do you write domain and range?

Domain and range are always written from smaller to larger values or from left to right for domain and from bottom to the top of the graph for range.


5. How do you find the domain and range on a calculator?

Enter input in the specified box and click on the calculate button to display output.


Linear Programming Calculator | Handy tool to find Linear Programming

Linear Programming Calculator

By taking the help of Linear Programming Calculator, you will get the exact solution quickly. You have to provide all your conditions and functions as input in the respective fields and press the calculate button to get the answer in seconds.

Linear Programming Calculator: Learn the procedure to solve the linear programming of the given constraints. Our free handy linear programming calculator tool is designed to help people who want to escape from mathematical calculations. One who is willing to know the detailed process involved in solving the Linear Programming of a function can read the further sections of this article.

How to Solve Objective functions with Linear Constraints?

Here, you can see the simple guidelines to solve the objective function with the given linear constraints. Follow these steps and compute the maximum and minimum of the functions.

  • Take any objective function P and other linear constraints
  • Out of all the constraints, compute the conditions which are having two variables for example x and y
  • Convert the expression as bring one variable y
  • By taking the slope of those constraints draw a graph
  • Mark the feasible region and find out the vertices
  • Substitute all the values of vertices in the objective function
  • Check for which vertices, the function is minimum and maximum

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 feasible region for 2x+y=1000, 2x+3y=1500, x=0, y=0 and maximize and minimize for the objective function 50x+40y?

Answer:

Given that,

Objective function f(x,y)=50x+40y

Given constraints are

2x+y=1000, 2x+3y=1500, x=0, y=0

2x+y=1000

y=1000-2x

2x+3y=1500

3y=1500-2x

y=(1500-2x)/3

y=500-2x/3

The graph will be

The shaded area will be the feasible region in the above graph

The vertices are (0,500), (375,250), (500,0)

f(x,y)=50x+40y

Substitute the vertices in the objective function

f(0,500)=50*0+40*500=20,000

f(375,250)=50*375+40*250=28,750

f(500,0)=50*500+40*0=25,000

The minimum value is (0,500)

Maximum values are (275,250)

FAQ’s on Linear Programming

1. What is the process of linear programming?

Linear programming is the process of taking various linear inequalities relating to some situation and finding the best value obtained under those conditions.


2. What is the linear function and examples?

Linear functions are graphs as a straight line format. The standard form of linear function is y=f(x)=a+bx. It has one dependent variable and one independent variable.


3. What are the components of linear programming?

The three different equalities or inequalities or components of the linear programming are decision variables, objective function and constraints.


4. How can you solve the linear programming problem?

Find out the feasible region for the constraints and decision variables. Point out the vertices, and substitute those values in the objective function to get the maximize and minimize values.


5. How do you solve the maximum value in linear programming?

If linear programming can be optimized, an optimal value will occur at one of the vertices of the region representing the set of feasible solutions.


Inflection Point Calculator | Calculate Inflection Point

Inflection Point Calculator

Make use of this free handy Inflection Point Calculator to find the inflection points of a function within less time. Just enter function in the input fields shown below and hit on the calculate button which is in blue colour next to the input field to get the output inflection points of the given function in no time.

Inflection Point Calculator: Want to calculate the inflection point of a function in a simple way? Then you must try out this user friendly tool provided. It is one of the easiest ways that you ever find to compute the inflection point of a function. This page is all about Finding Inflection Point of the given function using a simple method and the interactive tutorial explaining each step of the process.

Steps to Find Inflection Point

Follow the below provided step by step process to get the inflection point of the function easily.

  • Take any function f(x).
  • Compute the first derivative of function f(x) with respect to x i.e f'(x).
  • Perform the second derivative of f(x) i.e f”(x) and also solve the third derivative of the function.
  • f”'(x) should not be equal to zero.
  • Make f”(x) equal to zero and find the value of variable.
  • Substitute x value in the third derivative of function to know the minimum and maximum values.
  • Replace the x value in the given function to get the y coordinate value.
  • Then, inflection points will be (x value, obtained value from function).

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Example

Question: Find the inflection points for the function f(x) = -x4 + 6x2?

Solution:

Given function is f(x) = -x4 + 6x2

f'(x) = -4x3 + 12x

f”(x) = -12x2 + 12

f”'(x) = -24x

f”(x) = 0

-12x2 + 12 = 0

12 = 12x2

Divide by 12 on both sides.

1 = x2

x = ± 1

x1 = 1, x2 = -1

Substitute x = ± 1 in f”'(x)

f”'(1) = -24(1) = -24 < 0, then it is left hand bit to right hand bi.

f”'(-1) = -24(-1) = 24 > 0, then it is left hand bit to right hand bit.

Replace x = ± in f(x)

f(1) = -1+6 = 5

f(-1) = -1 +6 = 5

Therefore, inflection points are P1(, 5), P2(-, 5)

FAQs on Inflection Point Calculator

1. How do you find inflection points on a calculator?

Provide your input function in the calculator and tap on the calculate button to get the inflection points for that function.


2. What does inflection point mean?

Inflection point is defined as the point on the curve at which the concavity of the function changes. It can be a stationary point but not local maxima or local minima.


3. Find the point of inflection for the function f(x) = x5 – 5x4?

Given that

f(x) = x5 – 5x4

f'(x) = 5x4 – 20x3

f”(x) = 20x3 – 60x2

f”'(x) = 60x2 – 120x

Neccessary inflection point condition is f”(x) = 0

20x3 – 60x2 = 0

20x2(x-3) = 0

x1 = 0, x2 = 3

Substitute x2 = 3 in the f(x)

f(3) = 35 – 5*34 = 243 – 405 = -162

Inflection Point is (3, -162).


4. What is the difference between inflection point and critical point?

A critical point is a point on the graph where the function’s rate of change is altered wither from increasing to decreasing or in some unpredictable fashion. Inflection point is a point on the function where the sign of second derivative changes (where concavity changes). A critical point becomes the inflection point if the function changes concavity at that point.


Function Calculator | Online Calculator to solve Functions

Want any assistance in solving the given function? Then, make use of this Function Calculator. This is best option for you as it gives accurate answers in fraction of seconds. Simply provide your input as the function and press on the calculate button of the calculator to avail the output in no time.

Function Calculator: This best handy calculator generates the output as x-intercept, y-intercept, slope, curvature, derivative of the function. Students can get the step by step procedure on how to solve the functions in the following sections. Have a look at them and follow whenever required. You can obtain the result along with the detailed work so that you can learn and understand the concept.

Steps by Step Procedure to Solve Functions

Here is the simple method to solve the functions. Go through these steps and understand them to compute the function easily. Using these steps, you can find the slope, x-intercept, y-intercept, and derivative values of a function effortlessly.

  • Take any function
  • To compute the x intercept set y = 0 and solve the function
  • Set x = 0 to get the y intercept value.
  • To get the slope value convert the function into this form y = mx + c
  • Where m is the slope and c is the constant, the coefficient of y should be 1.
  • The derivative of a function can be computed by applying the derivative function and getting the value.

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Example

Question: Find the x-intercept, y-intercept, slope, derivative and curvature of the function f(x) = 3x – 10?

Solution:

Given Function is

f(x) = 3x – 10 = y

Set y = 0,

0 = 3x – 10

3x = 10

x = 10/3

(10/3, 0) is x-intercept.

Set x = 0,

y = 3(0) – 10

y = -10

(0, -10) is y-intercept.

Slope:

Convert the given function into y = mx + c form

y = 3x – 10

m = 3, c = -10

Slope is 3.

Curvature is 0.

Derivative of the function is

dy/dx = d/dx(3x – 10)

= d/dx(3x) – d/dx(10)

=3

x intercept is 10/3, y intercept is -10, slope is 3, curvature is 0, derivative is 3.

Frequently Asked Questions on Function Calculator

1. What are the functions?

Functions are defined as the equation where it gives one output for every input. Function is a mathematical rule that defines the relationship between dependent and independent variables.


2. How can you represent functions?

The standard form to represent the functions are f (x) = y.

Where, x is the input

y is the output of the desired function’F represents the function.


3. What is the difference between relation and function?

Relation means collection of inputs and outputs which are related to each other in some way. If each input of the relation having exactly one output, then that relation is called a function.


4. What is the domain and co domain of a function?

Domain of a function is the set of inputs for which the function is defined. A co domain is the set of possible output values of the function.


5. What are the different types of functions?

The different types of functions are Linear function, Quadratic function, Exponential function, Power function, Polynomial function, Logarithmic function, and so on.


Eigenvalue Calculator of a matrix | Tool for Eigenvalues

Eigenvalue Calculator of a matrix

Make use of this simple and straightforward calculator that offers the eigenvalues for a matrix. Eigenvalue Calculator takes the numbers i.e matrix in the input fields and generates the output in less amount of time by hitting the calculate button provided beside the input box.

Eigenvalue Calculator: Are you struggling to get the eigenvalues for matrix? Then, try this handy calculator tool and make your mathematical calculations immediately and easily. This calculator gives the detailed process of obtaining a solution to your question and the direct answer within fraction of seconds. We are also providing the examples, which are helpful to check whether the result is correct or not.

Simple Method To Find Eigenvalues

One of the best and shortest methods to calculate the Eigenvalues of a matrix is provided here. Checkout the simple steps of Eigenvalue Calculator and get your result by following them.




  • Take proper input values and represent it as a matrix.
  • Frame a new matrix by multiplying the Identity matrix contains v in place of 1 with the input matrix.
  • Find the determinant of the obtained matrix i.e multiplication of the diagonal values of a matrix and subtract the results.
  • The above process will form a characteristic polynomial.
  • Solve the equation to get the roots.
  • The obtained roots are eigenvalues for your input matrix.

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Example:

Question: Find the eigenvalues of a matrix ((-2,-4,2),(-2,1,2),(4,2,5))?

Solution:

Given matrix A= [(-2,-4,2),(-2,1,2),(4,2,5)]

To get the characteristic equation of matrix A, make

A-VI=0, where I is an Identity matrix.

Matrix=[(-2,-4,2),(-2,1,2),(4,2,5)]*[(v,0,0),(0,v,0),(0,0,v)]

Matrix=[(-2-v,-4,2),(-2,1-v,2),(4,2,5-v)]

Det Matrix=0

Det [(-2-v,-4,2),(-2,1-v,2),(4,2,5-v)]= 0

By expanding the determinant:

(-2-v)x[(1-v)x(5-v)-2×2]+4[(-2)x(5-v)-4×2]+2[(-2)x2-4(1-v)]=0

After simplifying

-v3+4v2+27v-90=0

or v3-4v2-27v+90=0

By applying trial and error method, we got

v3-4v2-27v+90=(v-3)(v2-v-30)

(v-3)(v2-v-30)=(v-3)(v+5)(v-6)

That means eigenvalues are 3,-5,6

FAQs on Eigenvalue Calculator

1. Does every matrix have eigenvalues?

Every matrix has an eigenvalue, but it may be a complex number.


2. What does a zero eigenvalue means?

Geometrically, zero eigenvalue means no information in an axis. We all know that the determinant of a matrix is equal to the products of all eigenvalues. If one or more eigenvalues are zero then the determinant is zero and which is a singular matrix.


3. Are eigenvalues unique?

Eigenvalues are not unique.


4. What is the eigenvalue of a matrix?

Eigenvalues are the special set of scalars associated with a linear system of equations known as characteristic roots and values.


Limit Calculator | Process to calculate the Limit Function

Limit Calculator

Use this online Limit Calculator to know the limit of a function by replacing the variable value. Enter your function and variable value as the inputs in the below fields and get the result by tapping on the calculate button in a fraction of seconds.

Limit Calculator: Are you looking for easy ways to find function limits? Then, stop your search right here because we have come up with a simple method to compute the function limit in the given range. With the help of this handy Limit Calculator tool, you can easily calculate the limit and know the output automatically. Furthermore, you can also check the steps to solve the function limit with a best example and its form.

How to get the Limit of a function?

The limits are used to define the integrals, derivatives, and continuity. The limit function is a concept in the analysis which concerns the behavior of a function at the particular moment. Here we are offering the stp by step process to evaluate a limit function. Checkout the below sections and follow them while calculating a limit function in the given range.

  • Take a limit function and substitute the variable value to get the output this is called substitution.
  • If the above substitution method fails, then follow this factorization method. Especially, use this method when the function is a polynomial expression.
  • Do factorization of the given function, cancel the similar terms and substitute the variable value.
  • When a function is having the square root in the numerator and polynomial expression in the denominator, solve it by rationalizing the numerator.
  • Solve the expression and substitute the variable value in it.

Basic Form

The standard form to represent the limit function is lim x to c f(x) = L

Where,

C is a real number

f is a real valued function

Example:

Question1: Solve Lim x->5 x^2-6x+8 / x-4?

Answer:

Here we use the substitution method

f(x)=x^2-6x+8 / x-4

f(5) = 5^2 – 6*5 + 8 / 5-4 = 25-30+8 / 1 = 3

Therefore, the solution is 3.

Question2: Solve lim x->4 x^2-6x+8 / x-4?

Answer:

f(x)=x^2-6x+8 / x-4

Substitution process does n’t work here. Because the denominator can’t be zero.

Check out the factorization method

After factorization the f(x) can be as follows

f(x) = (x-4) * (x-2) / (x-4)

After cancelling f(x) = x-2

f(4) = 4-2 = 2

The answer is 2

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Frequently Asked Questions on Limit

1. What is the limit formula?

lim x->a f(x) is the limit formula. This is called the limit of a function f(x) at an interval x=a.


2. What are the five laws of limits?

The list of limit laws are here.

  • Constant Law limx->a k=k.
  • Identity Law limx->a x=a.
  • Sum Law limx->a f(x)+g(x) = limx->af(x) + limx->ag(x)
  • Difference Law limx->a f(x)-g(x) = limx->af(x) – limx->ag(x)
  • Constant Coefficient Law limx->a k*f(x) = klimx->af(x)
  • Multiplication Law limx->a f(x)*g(x) = limx->af(x) * limx->ag(x)

3. What is the limit of a constant?

The limit of a constant function is always a constant.


4. What is the limit?

In maths, a limit is the value that a function approaches as the input and approaches some value.


5. Solve limx->13 square root (x-4)-3 / x-13 using the rationalizing the numerator process?

After rationalizing the numerator, we will get the expression as 1 / square root of x-4 +3. Substitute the value. the value is 1/16.


Laplace Transform Calculator | Quick & Easy Process

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.

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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.


Infinite Series Calculator | Find Sum of Infinite Series

Infinite Series Calculator

Avail Infinite Series Calculator Over here to solve your complex problems too easily. Simply provide the inputs in the respective input field and tap on the calculate button to get the concerned output.

Infinite Series Calculator: Finding the sum of an infinite series of a function is not so simple or easy for any one. It will have difficult mathematical operations and it consumes your time and energy. So, we are coming up with the best solution for your problem by giving the free handy Infinite Series Calculator tool. You can also get the lengthy manual solution to solve the sum of the infinite series of a function. Make use of this free calculator tool to get accurate solutions for your function quickly.

Steps to find the Sum of Infinite Series of Function

Learn about how to solve the sum of infinite series of a function using this simple formula. Follow the below provided step by step procedure to obtain your answer easily.

  • Take any function with the range to infinity to solve the infinite series
  • Convert that function into the standard form of the infinite series
  • Apply the infinite series formula
  • Do all the required mathematical calculations to get the result

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.

Standard Form of Infinite Series

Infinite series is defined as the sum of values in an infinite sequence of numbers. The notation Sigma (Σ) is used to represent the infinite series. The standard form of infinite series is

Σ0 rn

Where 0 is the lower limit

∞ is the upper limit

r is the function

The formula to find the infinite series of a function is defined by

Σ0 rn = 1/(1-r)

Example:

 

Question: solve the sum of Σ0 1/10n?

 

Solution:

Given function is 1/10n

r=1/10

Infinite series formula is

Σ0 rn = 1/(1-r)

Σ0∞ 1/10n=1/(1-1/10)

=10/9

Σ0∞ 1/10n=10/9

Frequently Asked Questions on Infinite Series Calculator

1. Can an infinite series be calculated?

We can calculate the sum of an infinite geometric series. The formula to solve the sum of infinite series is related to the formula for the sum of first n terms of a geometric series. Finally, the formula is Sn=a1(1-rn)/1-r.


2. What is the general formula for the sum of infinite geometric series?

The formula to find the sum of an infinite geometric series is S=a1/1-r.


3. What is r in a sequence?

r is called common ratio. The number multiplied or divided at each stage of a geometric seque is the common ratio.


4. What are the 4 types of sequences?

Some of the sequences are Arithmetic Sequences, Geometric Sequences, Harmonic Sequences, and Fibonacci Numbers.


5. What is meant by sequence and series?

Sequence is a list of numbers that have been ordered sequentially. Series is defined as the sum of the sequence terms.


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.

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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.