I've been stuck on the following problem: If S is a closed surface that bounds the volume V, prove that: integral over this surface dS = 0. I've been reading several textbooks that discuss flux, Stokes' Theorem, Divergence Theorem, but I can't seem to relate them to the problem I'm doing. The examples in the text all have a vector F and present the integral: integral over a surface of F dS, which I understand it as the flux. Is my case a flux problem? There is no vector F given in my problem. Should I divide the closed surface into two halves and argue that pairs of normal vectors, one from each half cancel and therefore the integral over this surface dS = 0? What about Stokes' Theorem -- transforming it into a line integral? Thanks.