Stokes' Theorem

Definition

Let $S$ be a smooth surface in ${\mathbb{R}}^3$ with boundary $C$, and a vector field $F(x,y,z)=F(P(x,y,z),Q(x,y,z),R(x,y,z))$. Then, ${\oint }_{C}Fdr={\iint }_S(\nabla \times F)\cdot dS$