Chapter 5.3, Problem 144E

In the following exercises, the integrals have been converted to polar coordinates. Verify that the identities aie true and choose the easiest way to evaluate the integrals, in rectangular or polar coordinates.

144. ${\displaystyle \underset{1}{\overset{2}{\int }}{\displaystyle \underset{0}{\overset{x}{\int }}\left(x^2+y^2\right)dydx={\displaystyle \underset{0}{\overset{\frac{\pi }{4}}{\int }}{\displaystyle \underset{0}{\overset{2\sec \theta }{\int }}{r}^{3}drd\theta }}}}$