I am currently trying to prove:
S = ∫∫a2sinΦdΦdθ
Here is my work (note that in my work I use dS instead of S, this is an accident):
I end up with:
S = ∫∫a*da2sinΦdΦdθ
Where da is the infinitesimal thickness of the surface.
Why am I getting the wrong answer?