MATLAB: how to solve this integral for getting expected value?

Question

I want to solve the expected value for f(x) with x=[x1,x2] follows uniform distribution. I tried this:

syms x r d x1 x2;
f=2*x*acos(x^2-d^2/2*x*(r+d)+d/x)*(1/sqrt(2*pi))*exp(-x^2/2);
int(f,'x',x1,x2)

I need a parametric approach. But Matlab fails to solve this integration in symbolic format. Any solution to that?

Answer 1

If you want to do it numerically, you need to use a numerical function: integral

example:

d=40;r=15;
%define f as anonymous function 
f=@(x)2.*x.*acos(x.^2-d^2./2.*x.*(r+d)+d./x).*(1/sqrt(2*pi)).*exp(-x.^2/2);
integral(f,40,70)

This gives me 0, (because it is 0), but if you try, for example:

d=4;r=2
integral(f,0,10)

ans =

   2.4036 - 3.3624i