$($a$)$ Given the double integral ${\displaystyle \underset{-4}{\overset{0}{}}}{\displaystyle \underset{-\sqrt[\phantom{2}]{x+4}}{\overset{\sqrt[\phantom{2}]{x+4}}{}}}2xdydx+{\displaystyle \underset{0}{\overset{5}{}}}{\displaystyle \underset{x-2}{\overset{\sqrt[\phantom{2}]{x+4}}{}}}2xdydx.$

$($i$)$ Rewrite the double integral by changing the order of integration.

$($ii$)$ Evaluate the double integral from part $($a$)($i$).$

$($b$)$ Given a solid bounded by the surfaces $z=-y,y=3,z=4-x^2$ and $z=x^2-4.$

$($i$)$ Setup a triple integral that can best describe the volume of the solid.

$($ii$)$ Compute the volume of the solid.

$[9$ Marks$]$