Chapter 6.8, Problem 422E

For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D.

422. [T] Use a CAS and the divergence theorem to evaluate ${\displaystyle {\iint }_{s}F\cdot dS}$ , Where $F\left(x,y,z\right)=\left(2x+y\cos z\right)i+\left(x^2-y\right)j+y^{2}zk$ and S is sphere $x^2+y^2+z^2=4$ orientated outward.