Use spherical coordinates to evaluate the integral,

${\displaystyle \underset{-2}{\overset{2}{}}}{\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{4-x^2}}{}}}{\displaystyle \underset{\sqrt[\phantom{2}]{x^2+y^2}}{\overset{2+\sqrt[\phantom{2}]{4-x^2-y^2}}{}}}zdzdydx$