Can anyone tell me whether or not the divergence theorem requires a conservative vector field? On a practice exam my professor gave a vector field that was nonconservative (I checked the curl) and proceeded to perform the divergence theorem to find the flux. On one of my homework problems I forgot to check whether the field was conservative and it turns out that field was nonconservative but still got the correct answer. I don't know if that is a fluke or not. In short: Do you need a conservative vector field in order to use the divergence theorem?