Sunday, August 13, 2023

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 


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