Chapter 6.7, Problem 363E

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

363. [T] Use a CAS to evaluate ${\displaystyle {\iint }_{s}curl\left(F\right)\cdot dS}$ , where $F\left(x,y,z\right)=2zi+3xj+5yk$ and S is the surface parametrically by $r\left(r,\theta \right)=r\cos \theta i+r\sin \theta j+\left(4-r^2\right)k$

$\left(0\le \theta \le 2\pi ,0\le r\le 3\right)$ .