MATLAB: Is there a method for numerical integration with some symbolic variables

integrationMATLAB

I wanna evaluate integral like the following,
The symbolic integral doesn't work well.
Is there a method to evaluate this integral with the dependence of m and M surviving?
My ultimate goal is to equating this integral with some function in order to find .

Best Answer

Since a closed-form symbolic solution does not exist, you will need to use a numerical method. You cannot get a simple expression; however, you can create an anonymous function which "acts" like an expression in terms of m and M.
f = @(s, m, M) sqrt(s)./((s-m.^2).^2+3*s).*exp(-s./M.^2);
f_int = @(m, M) integral(@(s) f(s, m, M), 0.07, 1.5);
Run it like this
>> f_int(1, 1)
ans =
    0.2519
>> f_int(1, 2)
ans =
    0.4109
You can then use it to solve for the equation using fsolve().
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