Is there a method for numerical integration with some symbolic variables?

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 .

Answer 1

[Ameer Hamza]

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().

[jisu kim]

Thanks for answering me. It helps very much for me. I solved the problem with your answer.

[Ameer Hamza]

I am glad to be of help!