Chapter 16.8, Problem 1E

A hemisphere $H$ and a portion $P$ of a paraboloid are shown. Suppose $F$ is a vector field on ${ℝ}^3$ whose components have continuous partial derivatives. Explain why

${\displaystyle \underset{H}{\iint }\text{curl }F}\cdot dS={\displaystyle \underset{P}{\iint }\text{curl }F\cdot \text{dS}}$