Chapter 14.3, Problem 28E

Converting to Polar Coordinates:

In Exercises 27 and 28, combine the sum of the two iterated integrals into a single iterated integral by converting to polar coordinates. Evaluate the resulting iterated integral.

${\displaystyle {\int }_0^{\raisebox{1ex}{$5\sqrt{2}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\displaystyle {\int }_0^{x}xydydx}}+{\displaystyle {\int }_{\raisebox{1ex}{$5\sqrt{2}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}^5{\displaystyle {\int }_0^{\sqrt{25-x^2}}xydydx}}$