Given the integral ${\displaystyle \underset{0}{\overset{\frac{1}{4}}{}}}{\displaystyle \underset{y^2}{\overset{\sqrt[\phantom{2}]{y}}{}}}xydxdy+{\displaystyle \underset{\frac{1}{4}}{\overset{\frac{1}{\sqrt[\phantom{2}]{2}}}{}}}{\displaystyle \underset{y^2}{\overset{\frac{1}{2}}{}}}xydxdy.$

a$)$ Sketch the region of integration.

b$)$ Evaluate integration by reversing the order of the integration.