Chapter 14, Problem 34RE

Converting to Polar Coordinates Write the sum of the two iterated integrals as a single iterated integral by converting to polar coordinates. Evaluate the resulting iterated integral.

${\displaystyle {\int }_0^{8/\sqrt{13}}{\displaystyle {\int }_0^{3x/2}xydydx+{\displaystyle {\int }_{8/\sqrt{13}}^4{\displaystyle {\int }_0^{\sqrt{16-x^2}}xydydx}}}}$