Chapter 14.7, Problem 41E

Choosing a more convenient surface The goal is to evaluate $A={\displaystyle {\iint }_S\left(\nabla \times F\right)\cdot ndS}$, where F = 〈yz, –xz, xy〉 and S is the surface of the upper half of the ellipsoid x² + y² + 8z² = 1(z ≥ 0).

a.    Evaluate a surface integral over a more convenient surface to find the value of A.

b.    Evaluate A using a line integral.