Use the divergence theorem to calculate the surface integral

$$S

F $$ dS;

that is$,$ calculate the flux of F across S$.$

F$($x$,$ y z$)=(7$xy $$ z$2)$i $+2$x$3$

z

$$j $+(7$xy $+$ z$2)$k$,$

$$ S is the surface of the solid bounded by the cylinder

x $=$ y$2$

and the planes

x $+$ z $=1$

and

z $=0$