$(6)$

$(a)$ Evaluate the integral ${}_D(x^2+y^2+z^2{)}^{2}dV$ where $D=\{(x,y,z)$:$x^2+y^2+z^{2}1\}is$

the unit ball. $(Hint$: use spherical coordinates.$)$ The unit ball $is$ a solid sphere $of$ radius

$1$ centered $at$ the origin.

$(b)$ Evaluate the integral ${}_D\frac{e^{-z}}{\sqrt[\phantom{2}]{x^2+y^2+z^2}}dV$ where $Dddd.{}_{D}zdV$ where $Dis$ the unit ball. Hint: exploit symmetry. $It$

$is$ possible $to$ evaluate this triple integral with a minimum $of$ computation!