If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.
- Samuel Dominic Chukwuemeka

For in GOD we live, and move, and have our being. - Acts 17:28

The Joy of a Teacher is the Success of his Students. - Samuel Dominic Chukwuemeka

# Integral Calculus Calculators

I greet you this day,
I wrote the codes for some of the calculators using JavaScript, a client-side scripting language.
The Wolfram Alpha widgets (many thanks to the developers) were used for some calculators.
Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me.
If you are my student, please do not contact me here. Contact me via the school's system.
Thank you for visiting.

Samuel Dominic Chukwuemeka (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S

## 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.

(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.

(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

(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

(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)

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

(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: