Activity 13.14.3

Find the flux of the vector field $\vF = \langle 3x^2+y^5,5+e^{z^3},z\rangle$ through the surface of the solid cube $Q$ in $\R^3$ with $-2\leq x\leq 2$, $-2\leq y\leq 2$, and $-2\leq z\leq 2$.

Find the flux of the vector field $\vG = \langle x^3,y^3,z^3\rangle$ through surface consisting of the top half of sphere of radius $3$ centered at the origin and the disc of radius $3$ in the $xy$-plane (centered at the origin).