I am having problem with an integral. I dont know how to write in mathcode so excuse me for my notation.
This is in spherical coordinates:
x = theta
y = psi
r = radial component
the integrand is: (cos(x)/r^2)
I want to integrate this over a solid angle of an arbitrary surface.
da is a differential area. And in spherical coordiantes should be: da = r^2*sin(x)dxdy
I know the integral should be 4*pi but I dont get it right. I want to have the antiderivate as (cos(x)^2)/2 from 0 to pi.
Then I get for the whole integral: 1/2*2pi = pi
So I am missing a factor 4 here. Can anyone help me show what I've missed?