Solving Integral Equations

Solving Integral Equations

Solving integral equations (for the variable A) of any of the following forms:

∫( f(x) dx, x = constant to x = A) = area

∫( f(x) dx, x = A to x = constant) = area

∫( f(x) dx, x = constant to x = constant) = A

is fairly easy with the solve feature on non-graphing scientific calculators such as:

Casio fx-115ES Plus 

Casio fx-991EX

Casio fx-991CW

TI-30X Pro Math Print

TI-36X Pro

The screen shots below show an example, from the Casio fx-991CW (Equation - Solver):

The function must have the variable x as the independent variable. We can designated any other variable to be limit to be solved for; I used the variable a.  

Here, we don't have to worry about the value of x when solving the equation because x is considered a dummy variable in the integral.  

Examples

Solve for A.

Example 1:

∫( e^(-x^2) dx, x = 0 to x = A) = 0.7

Casio fx-991EX:  

A = 0.8861430055,  L-R = 0

TI-30X Pro MathPrint:  

A = 0.8861430055201,  L-R = 0  (this solve took a little time)

Example 2:

∫( e^(-x^2) dx, x = A to x = 2) = 0.13

Casio fx-991EX:  

A = 1.014499933,  L-R = 0

TI-30X Pro MathPrint:  

A = 1.014499933366,  L-R = 0  

Example 3:

∫( A*x + 1 dx, x = 1 to x = 5 ) = 10

Casio fx-991EX:  

A = 0.4,  L-R = 0

TI-30X Pro MathPrint:  

A = 0.4,  L-R = 0  

Eddie 

All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.