$[21$ pt$]$ Compute the following iterated integral

a$.{\displaystyle \underset{0}{\overset{2}{}}}{\displaystyle \underset{\frac{}{2}}{\overset{1}{}}}\frac{1}{1+x^4}dxdy$

b$.{\displaystyle \underset{0}{\overset{4}{}}}{\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{16-x^2}}{}}}{\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{16-x^2-y^2}}{}}}{z}^{2}dzdydx$