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How to Solve an Equation with an Integral for the Integral Range Parameter?

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Benjamin on 26 Nov 2020
Commented: Benjamin on 26 Nov 2020
Dear experts,
I need to solve an equation that includes an integral in it, and I need to solve it for the parameter x that is the integral range. Please look at the picture attached. Note that I need to solve for a given L to see what is the value of s (or x).
I appreciate your response


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Accepted Answer

Star Strider
Star Strider on 26 Nov 2020
The gammainc function does not take complex arguments, so this is likely the best you can hope for:
F = @(S) S - 0.01 * gammainc(5/3, 40*S^0.6);
Lfcn = @(x) integral(@(S) 1./sqrt(F(S)), 0, x, 'ArrayValued',1);
Ssln = fsolve(@(x)abs(Lfcn(x)) - 0.2, 1E-8);
with x=0.0157.


Benjamin on 26 Nov 2020
It is very nice of you. I also posted another related question HERE. I appreciate if you also take a look at it.
Kind regards,

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