Divergence Theorem

Definition

Let $V$ be a subset of ${\mathbb{R}}^3$ with piecewise smooth boundary $S$, and a vector field $F(x,y,z)=F(P(x,y,z),Q(x,y,z),R(x,y,z))$ ${\iiint }_V(\nabla \cdot F)\cdot dV={\iint }_{S}F\cdot dS$