Question: "Region V, of unit volume, is bounded by the closed surface S. Given the vector field $\mathbf{F}=\langle 7x,2y,5z\rangle$, evaluate:
$$\int_S \mathbf{F}\cdot\mathbf{dS}$$
I guessed that by "unit volume" the question refers to a unit cube(?), but I can't get the right answer out and I'm really pretty stuck. Any help would be appreciated. Thanks!
Hint: use the divergence theorem.(What is the divergence of your vector field?)
You don't need to know what the region V looks like (i.e., you definitely don't need to assume it is a unit cube); you just need to know its volume.