Chapter 6.7, Problem 366E

For the following application exercises, the goal is to evaluate $A={\displaystyle {\iint }_s(\nabla \times \text{F})}\cdot \text{n}dS$ , where $\text{F}=\langle xz,-xz,xy\rangle$ and $S$ is the upper half of ellipsoid $x^2+y^2+8z^2=1$ , where $z\ge 0$ .

366. Evaluate $A$ using a line integral.