Question $5(25$ marks$)$

$($a$)$ Evaluate the following double integral by change of variable using polar coordinates

${\displaystyle \underset{-2}{\overset{0}{}}}{\displaystyle \underset{-\sqrt[\phantom{2}]{4-x^2}}{\overset{\sqrt[\phantom{2}]{4-x^2}}{}}}(x^2+y^2{)}^{\frac{3}{2}}dydx.$

$(9$ marks$)$