Let ${\mathbf{e}}_{\mathbf{r}}$ be the unit radial vector and $r=\sqrt{x^2+y^2+z^2}$.
Calculate the integral of $\mathbf{F} = e^{-r} {\mathbf{e}}_{\mathbf{r}}$ over:

(a) The upper-hemisphere of $x^2+y^2+z^2=9$ , outward-pointing normal
(b) The region on the sphere of radius $r=6$ centered at the origin that lies inside the first octant $x,y,z \ge 0$

(a) $\iint_S \mathbf{F} \cdot d\mathbf{S} =$

(b) $\iint_S \mathbf{F} \cdot d\mathbf{S} =$