Vector field F is given by

F $($r$)=($x$+2,0,$z$+2)$

and surface A is the locus of points satisfying z$+$ x$2+$ y$2=3+2$ x$2+$ y$2$ for z $0.($Note

that the positive square root appears in this expression.$)$

$($b$)$ Evaluate directly $($using cylindrical coordinates or otherwise$)$ the surface integral

I$=$

F$$dS

A

where the flux is evaluated in the direction with positive z component.