1. The problem statement, all variables and given/known data I have a vector function, and I need to take the surface integral of it over a hemisphere, top half only. I'm "confirming" the divergence theorem by doing a volume integral and surface integral. Already did the volume one so I have something to compare to already. 3. The attempt at a solution Yeah yeah, "look at your book!" I've checked my calc book, my mathematical physics book, and my E&M book (which assigned the problem) and for some reason I just can't get it. EDIT: Also, I should mention that the vector isn't given in "i,j,k" form, but "r, theta, phi", which is even more confusing for me. The books either use a simple cube (ya thanks) or cylindrical coordinates, which still makes it easier for me to grasp. Let me see if I am thinking of this correctly: dS will be d(theta)d(phi) for the top half, and should be d(r)d(phi) for the disk (My phi goes from 0 to 2pi). However I think I am missing something (Jacobian?). Besides that, I need to dot the function vector with the normal vector, yes? The book says I need to take the gradient of the surface function (and normalize it) to make it a normal vector. So for the top half it would just be <r,0,0>? And I can't figure it out for the disk at the bottom. I guess I could use -k and then just transformed into spherical coordinates?