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.