극좌표 변환: x^2+y^2=r^2, dA=rdrd\theta. 영역 R은 0 \le r \le 2이고 0 \le \theta \le 2\pi이다.

\displaystyle \iint_{R} \sqrt{r^2}rdrd\theta = \displaystyle \int_{0}^{2\pi} \int_{0}^{2} r^2drd\theta

= \displaystyle \int_{0}^{2\pi} \left[ \dfrac{1}{3}r^3 \right]_{0}^{2} d\theta = \displaystyle \int_{0}^{2\pi} \dfrac{8}{3}\,d\theta

= \dfrac{8}{3} \left[ \theta \right]_{0}^{2\pi}= \dfrac{8}{3}(2\pi) = \dfrac{16\pi}{3}