Chapter 6.8, Problem 417E

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.

417. [T] Use a CAS to find the flux of vector field $F\left(x,y,z\right)=\left(e^y+x\right)i+\left(3\cos \left(xz\right)-y\right)j+zk$ through surface S, where S is given by $z^2=4x^2+4y^2$ from $0\le z\le 4$ , oriented so the unit normal vector points downward.