Answer
$\overline{x}=0, \overline{y}=\dfrac{a \pi}{4}$
Work Step by Step
We notice that the center of mass is symmetric about the y- axis, so $\overline {x}=0$
and $\overline{y}=\dfrac{ m_x}{m}=\dfrac{\int_0^{\pi} a \sin \theta \delta a d\theta}{\int_0^{\pi} \delta a d\theta} $
or, $=\dfrac{\int_0^{\pi} a^2 k \sin^2 \theta d\theta}{\int_0^{\pi} ak \sin \theta d\theta} $
or, $=\dfrac{a (\theta-\sin (2 \theta/2)]_0^{\pi}}{(2)(2)} $
or, $\overline{y}=\dfrac{a \pi}{4}$
