Chapter 6.7, Problem 342E

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

342. [T] Use a CAS and Stokes’ theorem to evaluate ${\displaystyle {\iint }_{s}curlF\cdot dS}$ , where $F\left(x,y,z\right)=z^{2}i-3xyj+x^3{y}^{3}k$ and S is the top part of $z=5-x^2-y^2$ above plane $z=1$ , and S is oriented upward.