Answer
$\frac{81\pi}{5}$
Work Step by Step
$\int\int_{D}(x^{2}+y^{2})^{3/2}dA=\int_{0}^{\pi/3}\int_{0} ^{3} r^{3}rdrd\theta$
$=\int_{0}^{\pi/3}\frac{ r^{5}}{5}|_{0}^{3}d\theta$
$=\int_{0}^{\pi/3}\frac{ 3^{5}}{5}|d\theta$
$=\int_{0}^{\pi/3}\frac{ 243}{5}|d\theta$
$=[\frac{ 243}{5}\theta]|_{0}^{\pi/3}$
$=\frac{ 243}{5}(\pi/3-0)$
$=\frac{81\pi}{5}$
