So I understand the divergence theorem for the most part. This is the proof that I'm working with http://www.math.ncku.edu.tw/~rchen/Advanced Calculus/divergence theorem.pdf For right now I'm just looking at the rectangular model. My understanding is that should we find a proof for this model we can validate all transformations of the models from a proof regarding the integral values of transformed regions. (there's also probably an easier method where we just don't assume the object to be square too, right?) What bothers me is that the area integral of F(x,y,z) dot d(a) is equal to the double integral of F(x,y,z)dydz. What happened to the cos@ value that existed when we were dotting across the area? the other thing that is bothering me is that when we get rid of this dot product, one the integrals becomes negative. What gives?