Section $17\mathrm{.}3$

Use the Divergence Theorem to evaluate the outward flux of the field $F(x,y,z)=($:$e^{z^2},4y+sin(x^{2}z),5z+\sqrt[\phantom{2}]{x^2+9y^2}$:$)$ through the surface $S,$ where $S$ is the region $x^2+y^{2}z8-x^2-y^2.$

$($Give an exact answer. Use symbolic notation and fractions where needed.$)$

Div$(F)=$

${}_{S}F*dS={}_W$Div$(F)dV=$

$($W is the solid entrapped inside the closed surface $S.)$