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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