Have you ever wondered why the divergence theorem doesn't apply to line integrals? That's because the definition of the line integral is somewhat flawed!
In this video, I generalize the notion of a surface integral so that it can be applied to line integrals (I call this a line-surface integral), and I show that, using this new definition, the divergence theorem applies and is just Green's theorem! So in this sense, the divergence theorem is a generalization of Green's theorem. Wow!!!
Note: In the video I use the notation integral over S of F . dr, but the notation integral over C of F . dS is more appropriate
