Chapter 6.7, Problem 339E

For the following exercises, use Stokes’ theorem to evaluate ${\displaystyle {\iint }_s\left(curlF\cdot N\right)dS}$ for the vector fields and surface.

339. Use Stokes’ theorem to evaluate ${\displaystyle {\iint }_{s}curlF\cdot dS}$ , where $F\left(x,y,z\right)=e^{xy}\cos zi+x^{2}zj+xyk$ , and S is half of sphere $x=\sqrt{1-y^2-z^2}$ , oriented out toward the positive x-axis.