This problem is to be solved by integration. One quarter of a square of side $a$ is removed $($see the figure$).$ What are the coordinates $\stackrel{}{x}$ and $\frac{?}{\text{b}\text{a}\text{r}}(y)$ of the centroid $C$ of the remaining area?

$($a$)$ Enter the coordinate $\stackrel{}{x}$ of the centroid $C.$

$($b$)$ Enter the coordinate $\frac{?}{\text{b}\text{a}\text{r}}(y)$ of the centroid $C.$