Chapter 6.8, Problem 382E

For the following exercises, use a computer algebraicsystem (CAS) and the divergence theorem to evaluate surface integral ${\displaystyle {\int }_{s}F\cdot ndS}$ for the given choice of F andthe boundary surface S. For each closed surface, assume Nis the outward unit normal vector.

382. [T] $F\left(x,y,z\right)=x{y}^{2}i+y{z}^{2}j+x^{2}zk$ ; S is the surface bounded above by sphere $\rho =2$ and below by cone $\phi =\frac{\pi }{4}$ in spherical coordinates. (Think of S as thesurface of an “ice cream cone”)