Is there an analog of the Kelvin-Stokes theorem for divergence? In other words, is it true that for a surface $S$, $\int_ {\partial S}} \vec {F} \cdot \hat {n} \; \mathrm {d} s= \iint_ {S} \nabla \cdot \vec {F} \; \mathrm {d} s$?
valid question