Let E be the solid bounded by the xy$-$plane and paraboloid

z $=4$ x$2$ y$2$

so that S is the surface of the paraboloid piece together with the disk in the xy$-$plane that forms its bottom.

If

F$($x$,$ y$,$ z$)=($xz sin$($yz$)+$ x$3)$i $+$ cos$($yz$)$j $+(3$zy$2$ ex$2+$ y$2)$k$,$

find

$$S

F $$ dS

using the divergence theorem.