Solve integral equation using MATLAB

Question

I would like to solve an equation below using MATLAB:

All the parameters except $p$ are known, so I only need to solve for $p$. However since I need to consider the sign of the integrand and there is an absolute value sign in it I don't know how to solve it. Could anyone please help?

Answer 1

Since $ p $ is a scalar you can try use MATLAB's fzero().

Try approximating the integral using a sum.
Write this as function of $ p $ and set it as a function handler.
Now just htrow it into fzero() (The integral minus 1).

As a starting point I'd also graph the function for various values of $ p $ just to see its behavior.