Answer
$\overline{x}=\dfrac{3\sqrt 3}{\pi} $ and $\overline{y}=0$
Work Step by Step
$M=\int_{-\pi/3}^{\pi/3} \int_{0}^3 r \ dr \ d \theta=\dfrac{9}{2} \int_{-\pi/3}^{\pi/3} d \theta = 3 \pi$
Now, $M_y=\int_{-\pi/3}^{\pi/3} \int_{0}^3 r^2 \cos \theta \ dr \ d \theta=(9) \int_{-\pi/3}^{\pi/3} \cos \theta d \theta = 9 \sqrt 3$ and $M_x=0$
So, $\overline{x}=\dfrac{3\sqrt 3}{\pi} $ and $\overline{y}=0$
