Let

F$($x$,$ y$,$ z$)=2$xi $3$xyj $+$ xz$2$k$.$

Use the divergence theorem to calculate

$$S

F $$ dS$,$

where S is the surface of the cube with corners at

$(0,0,0),$

$(1,0,0),$

$(0,1,0),$

$(1,1,0),$

$(0,0,1),$

$(1,0,1),$

$(0,1,1),$

and

$(1,1,1),$

oriented outward.