I "know" that you can use Green's theorem to integrate over a region bounded by a closed loop. But this is only if the vector field has continuous first partial derivatives inside the region.
So I thought that Stokes theorem allowed us to avoid the discontinuity in the 2D region by "going over it" using a 3D surface instead. Now that I have done numerous homework problems, I'm thinking I got this all wrong. It seems Stokes theorem is just a really hard way to doing Green's theorem.
Why would anyone use Stokes theorem instead of Green's theorem? Stokes is just more work!