Let $e_r$ be the unit radial vector and $r=\sqrt[\phantom{2}]{x^2+y^2+z^2}.$

Calculate the integral of $F=e^{-r}{e}_r$ over:

$($a$)$ The upper$-$hemisphere of $x^2+y^2+z^2=4,$ outward$-$pointing normal

$($b$)$ The region on the sphere of radius $r=2$ centered at the origin that lies inside the first octant $x,y,z0$

$($a$){}_{S}F*dS=$

$($b$){}_{S}F*dS=$