Chapter 17, Problem 60RE

Stokes’ Theorem for surface integrals Use Stokes’ Theorem to evaluate the surface integral ${\displaystyle {\iint }_S\left(\nabla \times F\right)}\cdot ndS$. Assume that n is the outward normal.

60.    F = 〈x² – z², y², xz〉, where S is the hemisphere x² + y² + z² = 4, for y ≥ 0