Chapter 6.8, Problem 416E

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.

416. [T] Use a CAS to find the flux of vector field $F\left(x,y,z\right)=zi+zj+\sqrt{x^2+y^2}k$ across the portion of hyperboloid $x^2+y^2=z^2+1$ between planes $z=0$ and $z=\frac{\sqrt{3}}{3}$ , oriented so the unit normal vector points away from the z-axis.