Integral Calculus Calculators

Calculators for Integrals

Indefinite Integrals

Use only $x$ and $y$
$x$ is the independent vavariable.
$y$ is the dependent variable.
Use $e$ and $h$ appropriately/accordingly

This calculator will:
(1.) Determine the antiderivative of a function (indefinite integral of the function).
(2.) Graph the antiderivative of the function.

To use the calculator, please:
(1.) Type the function in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed.
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed, into the small textbox of the calculator.
(5.) Click the "Submit" button.
(6.) Check to make sure that it is the correct function you typed.
(7.) Review the answers. At least one of the answers is probably what you need.

Using the Indefinite Integrals Calculator
Type: $7$ as 7
Type: $4x + 3$ as 4 * x + 3 * x
Type: $y = 4x + 3$ as y = 4 * x + 3
Type: $4x^3 - 5x^{\dfrac{1}{2}} + 7x^{-\dfrac{2}{3}}$ as 4 * x^3 - 5 * x^(1/2) + 7 * x^(-2/3)
Type: $y = 4x^3 - 5x^2 + 4$ as y = 4 * x^2 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $y = |-7 - 5x|$ as y = |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $y = \sec^2 x$ as y = sec^2 x
Type: $y = \cos hx$ as y = cos hx
Type: $y = \dfrac{1}{1 - x^2}$ as y = 1 / (1 - x^2)
Type: $y = \dfrac{-1}{\sqrt{1 - x^2}}$ as y = -1 / (sqrt(1 - x^2))

Integrate $wrt\;x$

Definite Integrals

Use only $x$ and $y$
$x$ is the independent vavariable.
$y$ is the dependent variable.
Use $e$ and $h$ appropriately/accordingly

This calculator will:
(1.) Calculate the definite integral of a function when given the lower limit and the upper limit of the integral.
(2.) Determine the antiderivative of a function (indefinite integral of the function).

To use the calculator, please:
(1.) Type the function in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed.
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed, into the small textbox of the calculator.
(5.) Type the lower and upper limits of integration in the two small textboxes of the calculator.
The first small textbox is the lower limit of integration.
The second small textbox is the upper limit of integration.
entre means "enter", y means "and"...got to learn Spanish 😊
(6.) Click the "CALCULAR YA..." button ("Calculate" button).
(7.) Check to make sure that it is the correct function you typed.
(8.) Review the answers. At least one of the answers is probably what you need.

Using the Definite Integrals Calculator
Type: $7$ as 7
Type: $4x + 3$ as 4 * x + 3 * x
Type: $y = 4x + 3$ as y = 4 * x + 3
Type: $4x^3 - 5x^{\dfrac{1}{2}} + 7x^{-\dfrac{2}{3}}$ as 4 * x^3 - 5 * x^(1/2) + 7 * x^(-2/3)
Type: $y = 4x^3 - 5x^2 + 4$ as y = 4 * x^2 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $y = |-7 - 5x|$ as y = |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $y = \sec^2 x$ as y = sec^2 x
Type: $y = \cos hx$ as y = cos hx
Type: $y = \dfrac{1}{1 - x^2}$ as y = 1 / (1 - x^2)
Type: $y = \dfrac{-1}{\sqrt{1 - x^2}}$ as y = -1 / (sqrt(1 - x^2))

Integrate $wrt\;x$

Average Value of a Function over an Interval

Use only $x$ and $y$
$x$ is the independent vavariable.
$y$ is the dependent variable.
Use $e$ and $h$ appropriately/accordingly

This calculator will:
(1.) Calculate the average value of a function over an interval of values.

To use the calculator, please:
(1.) Type the function in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed.
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed, into the small textbox of the calculator.
(5.) Type the lower limit and the upper limit of integration accordingly in the textboxes of the calculator.
(6.) Click the "Submit" button.
(7.) Check to make sure that it is the correct function you typed.
(8.) Review the answer.

Using the Average Value Calculator
Type: $7$ as 7
Type: $4x + 3$ as 4 * x + 3 * x
Type: $y = 4x + 3$ as y = 4 * x + 3
Type: $4x^3 - 5x^{\dfrac{1}{2}} + 7x^{-\dfrac{2}{3}}$ as 4 * x^3 - 5 * x^(1/2) + 7 * x^(-2/3)
Type: $y = 4x^3 - 5x^2 + 4$ as y = 4 * x^2 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $y = |-7 - 5x|$ as y = |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $y = \sec^2 x$ as y = sec^2 x
Type: $y = \cos hx$ as y = cos hx
Type: $y = \dfrac{1}{1 - x^2}$ as y = 1 / (1 - x^2)
Type: $y = \dfrac{-1}{\sqrt{1 - x^2}}$ as y = -1 / (sqrt(1 - x^2))

Function:

Double Integrals

This calculator will:
(1.) Determine the double integral of a function with respect to several variables.

To use the calculator, please:
(1.) Type the function in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed.
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed, into the small textbox of the calculator.
(5.) Select the two variables for which you want to find the antiderivative with respect to, as well as the order in which the integration is to be performed.
(6.) Type the lower and upper limits of integration for the first variable.
(7.) Type the lower and upper limits of integration for the second variable.
(8.) Click the "Submit" button.
(9.) Check to make sure that it is the correct function you typed.
(10.) Review the answers. At least one of the answers is probably what you need.

Using the Double Integrals Calculator
Type: $7$ as 7
Type: $4x + 3 - 2y$ as 4 * x + 3 * x - 2 * y
Type: $4x^3 - 5y^{\dfrac{1}{2}} + 7x^{-\dfrac{2}{3}}$ as 4 * x^3 - 5 * y^(1/2) + 7 * x^(-2/3)
Type: $4y^3 - 5x^2 + 4$ as 4 * y^3 - 5 * x^2 + 4
Type: $(-7x^3 - 2y^{-4})^{-3}$ as (-7 * x^3 - 2 * y^(-4))^(-3)
Type: $12e^{-3xy}$ as 12 * e^(-3 * x * y)
Type: $\dfrac{y^2}{1 - x^2}$ as y^2 / (1 - x^2)
Type: $\dfrac{-x}{\sqrt{1 - y^2}}$ as -x / (sqrt(1 - y^2))

Example: Integrate $wrt\;y\;\;then\;\;wrt\;x$

Double Integrals in Polar Coordinates

This calculator will:
(1.) Calculate the double integral of a function with respect to $r$, then with respect to $\theta$

To use the calculator, please:
(1.) Type the function in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed.
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed, into the small textbox of the calculator.
(5.) Type the lower and upper limits of integration for $r$.
(6.) Type the lower and upper limits of integration for $\theta$.
(7.) Click the "Submit" button.
(8.) Check to make sure that it is the correct function you typed.
(9.) Review the answers. At least one of the answers is probably what you need.

Using the Double Integrals in Polar Coordinates Calculator
Type: $7$ as 7
Type: $(r\sin\theta)r\;dr\;d\theta$ as r\sin\theta Do not include the "other" $r$ because it is already included in the calculator
Type: $(1 - r^2)r\;dr\;d\theta$ as (1 - r^2) Do not include the "other" $r$ because it is already included in the calculator
Type: $\pi$ as pi

Example: Integrate $wrt\;r\;\;then\;\;wrt\;\theta$

Triple Integrals

This calculator will:
(1.) Determine the triple integral of a function with respect to several variables.

To use the calculator, please:
(1.) Review all the directions of the previous integrals.

Using the Triple Integrals Calculator
Type: $7$ as 7
Type: $4x + 3 - 2y + 3z$ as 4 * x + 3 * x - 2 * y + 3 * z
Type: $4x^3 - 5y^{\dfrac{1}{2}} + 7z^{-\dfrac{2}{3}}$ as 4 * x^3 - 5 * y^(1/2) + 7 * z^(-2/3)
Type: $4y^3 - 5x^2 + 4z^4$ as 4 * y^3 - 5 * x^2 + 4 * z^4
Type: $(-7x^3 - 2y^{-4})^{-3}$ as (-7 * x^3 - 2 * y^(-4))^(-3)
Type: $12e^{-3xyz}$ as 12 * e^(-3 * x * y * z)
Type: $\dfrac{y^2}{z^2 - x^2}$ as y^2 / (z^2 - x^2)
Type: $\dfrac{-x}{\sqrt{1 - y^2}}$ as -x / (sqrt(1 - y^2))

Example: Integrate $wrt\;z\;\;then\;\;wrt\;\;y\;\;then\;\;wrt\;x$

Triple Integrals in Cylindrical Coordinates

This calculator will:
(1.) Calculate the triple integral of a function with respect to $z$, then with respect to $r$, then with respect to $\theta$

To use the calculator, please:
(1.) Type the function in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed.
(3.) Copy and paste the function you typed, into the small textbox of the calculator.
(4.) Type the lower and upper limits of integration for $z$.
(5.) Type the lower and upper limits of integration for $r$.
(6.) Type the lower and upper limits of integration for $\theta$.
(7.) Click the "Submit" button.
(8.) Check to make sure that it is the correct function you typed.
(9.) Review the answers. At least one of the answers is probably what you need.

Using the Triple Integrals in Cylindrical Coordinates Calculator
Type: $7$ as 7
Type: $(r\sin\theta)r\;dr\;d\theta$ as r\sin\theta
Type: $(1 - r^2)r\;dr\;d\theta$ as (1 - r^2)
Type: $z_{max} = r\cos\theta$ as r\cos\theta
Type: $\pi$ as pi

Example: Integrate $wrt\;z\;\;wrt\;r\;\;then\;\;wrt\;\theta$

Triple Integrals in Spherical Coordinates

This calculator will:
(1.) Calculate the triple integral of a function in spherical coordinates.

To use the calculator, please:
(1.) Review all the directions of the previous integrals.

Example:

Triple Integrals in Rectangular Coordinates

This calculator will:
(1.) Calculate the triple integral of a function in spherical coordinates.

To use the calculator, please:
(1.) Review all the directions of the previous integrals.

Example:

Calculators for Area Between Two Curves

Area Between Two Curves
The limits of integration are not given

Use only $x$ and $y$
$x$ is the independent vavariable.
$y$ is the dependent variable.
Use $e$ and $h$ appropriately/accordingly

This calculator will:
(1.) Calculate the lower limit and the upper limit of the integral.
(2.) Determine the area between two curves.
(3.) Graph the two curves and indicate the area between the curves.

To use the calculator, please:
(1.) Type the functions in the two textboxes (the bigger textboxes).
(2.) Type them according to the examples I listed.
(3.) Delete the "default" functions in the textboxes of the calculator.
(4.) Copy and paste the functions you typed respectively, into the small textboxes of the calculator.
(5.) Type the lower and upper limits of integration in the two small textboxes of the calculator.
The first small textbox is the lower limit of integration.
The second small textbox is the upper limit of integration.
(6.) Click the "Calculate" button.
(7.) Check to make sure that they are the correct functions you typed.
(8.) Review the answers. At least one of the answers is probably what you need.

Using the Area Between Two Curves (not given Limits) Calculator
Type: $4x + 3$ as 4 * x + 3 * x
Type: $y = 4x + 3$ as y = 4 * x + 3
Type: $4x^3 - 5x^2 + 4$ as 4 * x^3 - 5 * x^2 + 4
Type: $y = 4x^3 - 5x^2 + 4$ as y = 4 * x^2 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $y = |-7 - 5x|$ as y = |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $y = \sec^2 x$ as y = sec^2 x
Type: $y = \cos hx$ as y = cos hx
Type: $y = \dfrac{1}{1 - x^2}$ as y = 1 / (1 - x^2)
Type: $y = \dfrac{-1}{\sqrt{1 - x^2}}$ as y = -1 / (sqrt(1 - x^2))

First Function:

Second Function:

Area Between Two Curves
The limits of integration are given

Use only $x$ and $y$
$x$ is the independent vavariable.
$y$ is the dependent variable.
Use $e$ and $h$ appropriately/accordingly

This calculator will:
(1.) Determine the area between two curves between the given limits of integration.
(2.) Graph the two curves and indicate the area between the curves.

To use the calculator, please:
(1.) Type the functions in the two textboxes (the bigger textboxes).
(2.) Type them according to the examples I listed.
(3.) Delete the "default" functions in the textboxes of the calculator.
(4.) Copy and paste the functions you typed respectively, into the small textboxes of the calculator.
(5.) Click the "Submit" button.
(6.) Check to make sure that they are the correct functions you typed.
(7.) Review the answers. At least one of the answers is probably what you need.

Using the Area Between Two Curves (given Limits) Calculator
Type: $4x + 3$ as 4 * x + 3 * x
Type: $y = 4x + 3$ as y = 4 * x + 3
Type: $4x^3 - 5x^2 + 4$ as 4 * x^3 - 5 * x^2 + 4
Type: $y = 4x^3 - 5x^2 + 4$ as y = 4 * x^2 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $y = |-7 - 5x|$ as y = |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $y = \sec^2 x$ as y = sec^2 x
Type: $y = \cos hx$ as y = cos hx
Type: $y = \dfrac{1}{1 - x^2}$ as y = 1 / (1 - x^2)
Type: $y = \dfrac{-1}{\sqrt{1 - x^2}}$ as y = -1 / (sqrt(1 - x^2))

First Function:

Second Function:

Trapezoidal Rule and Simpson's Rule

Trapezoidal Rule

This calculator will:
(1.) Approximate the value of a definite integral using the Trapezoidal Rule

To use the calculator, please:
(1.) Type the function in the first textbox (the bigger textboxes).
(2.) Type it according to the examples I listed.
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed into the textbox of the calculator.
(5.) Type the Number of Trapezoids, and the Lower Limit and the Upper Limit of integration, in their respective textboxes of the calculator.
(6.) Click the "Submit" button.
(7.) Check to make sure that the function you typed is what you need.
(8.) Review the answers. At least one of the answers is probably what you need.

Using the Trapezoidal Rule Calculator
Type: $7$ as 7
Type: $\pi$ as pi
Type: $\theta$ as theta
Type: $4x + 3$ as 4 * x + 3 * x
Type: $4x^3 - 5x^2 + 4$ as 4 * x^3 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $|-7 - 5x|$ as |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $\sec^2 x$ as sec^2 x
Type: $\cos hx$ as cos hx
Type: $\dfrac{1}{1 - x^2}$ as 1 / (1 - x^2)
Type: $\dfrac{-1}{\sqrt{1 - x^2}}$ as -1 / (sqrt(1 - x^2))

Function:

Simpson's Rule (First Calculator)

This calculator will:
(1.) Approximate the value of a definite integral using the Simpson's Rule

To use the calculator, please:
(1.) Type the function in the first textbox (the bigger textboxes).
(2.) Type it according to the examples I listed.
(3.) Delete the "default" function in the textbox of the calculator.
(4.) Copy and paste the function you typed into the textbox of the calculator.
(5.) Type the Lower Limit and the Upper Limit of integration, and the Interval Size, in their respective textboxes of the calculator.
(6.) Click the "Submit" button.
(7.) Check to make sure that the function you typed is what you need.
(8.) Review the answers. At least one of the answers is probably what you need.

Using the Simpson's Rule Calculator
Type: $7$ as 7
Type: $\pi$ as pi
Type: $\theta$ as theta
Type: $4x + 3$ as 4 * x + 3 * x
Type: $4x^3 - 5x^2 + 4$ as 4 * x^3 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $|-7 - 5x|$ as |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $\sec^2 x$ as sec^2 x
Type: $\cos hx$ as cos hx
Type: $\dfrac{1}{1 - x^2}$ as 1 / (1 - x^2)
Type: $\dfrac{-1}{\sqrt{1 - x^2}}$ as -1 / (sqrt(1 - x^2))

Function:

Simpson's Rule (Second Calculator)

Using the Simpson's Rule Calculator
Type: $7$ as 7
Type: $\pi$ as pi
Type: $\theta$ as theta
Type: $4x + 3$ as 4 * x + 3 * x
Type: $4x^3 - 5x^2 + 4$ as 4 * x^3 - 5 * x^2 + 4
Type: $(-7x^3 - 2x^{-4})^{-3}$ as (-7 * x^3 - 2 * x^(-4))^(-3)
Type: $|-7 - 5x|$ as |-7 - 5x|
Type: $12e^{-3x}$ as 12 * e^(-3 * x)
Type: $(\ln x)^5$ as (log_e x)^5 Notice the underscore between log and e. Notice the space between e and x
Type: $(\log x)^5$ as (log x)^5
Type: $\sec^2 x$ as sec^2 x
Type: $\cos hx$ as cos hx
Type: $\dfrac{1}{1 - x^2}$ as 1 / (1 - x^2)
Type: $\dfrac{-1}{\sqrt{1 - x^2}}$ as -1 / (sqrt(1 - x^2))

Function:

Integral Calculus Calculators

Calculators for Integrals

Indefinite Integrals

Definite Integrals

Average Value of a Function over an Interval

Double Integrals

Double Integrals in Polar Coordinates

Triple Integrals

Triple Integrals in Cylindrical Coordinates

Triple Integrals in Spherical Coordinates

Triple Integrals in Rectangular Coordinates

Calculators for Area Between Two Curves

Area Between Two Curves The limits of integration are not given

Area Between Two Curves The limits of integration are given

Trapezoidal Rule and Simpson's Rule

Trapezoidal Rule

Simpson's Rule (First Calculator)

Simpson's Rule (Second Calculator)

Area Between Two Curves
The limits of integration are not given

Area Between Two Curves
The limits of integration are given