alright, this bit of homework has really got to me, so I will post the original question here, along with the work I've done. Please help me out guys:
Calculate the surface integral Where and S is the entire sphere with outward orientation
SO, the tip I got from lectures is that we are basically only considering F on S. So:
I redifined S in terms of spherical coordinates such that because the radius is a constant, I don't need to consider it (as independent) when I make the parameterized surface, since it is always 3. I can rewrite the integrals now as:
and, because I switched to spherical coordinates, I also need a jacobian of which, in this case, is
Now, I take the derivative of this separetly with respect to each variable, and then cross them (still the tips from the lectures), which would, effectively, be
okay, that all said, here is where it's my own brain, and I feel like I've missed something obvious, but here goes anyway.
for my varibles,
the fun part:
= and I have no idea where to go from here. I only combined like terms and pulled out a ... any helpful hints appreciated.