Let vec$($v$)=($:x$^(2)$z$,4-2$xyz$-3$y$+$x$^(2)$y$,3$z$-$x$^(2)$z:$)$ be the velocity field of a fluid. Compute the flux of vec$($v$)$

across the surface x$^(2)+$y$^(2)+$z$^(2)=4$ where y$>0$ and the surface is oriented away from the origin.

Hint: Use the Divergence Theorem.