(c) Whose theorem says that the double integral equals the line integral

Suppose $\mathbf{F}=M(x,y)\mathbf{i}+N(x,y)\mathbf{j}$, $R$ is a region in the $xy$ plane, and $(x,y,z)$ is in $V$ if $(x,y)$ is in $R$ and $|z|\ge 1$.

(a) Describe $V$ and reduce $\iiint ÷\mathbf{F}dV$ to a double integral.

(b) Reduce $\iint \mathbf{F}\cdot ndS$ to a line integral (check top, bottom, side).

(c) Whose theorem says that the double integral equals the line integral?

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §15.5 The Divergence Theorem, #21