Use integration to prove that the centroid of a quarter-circular area with radius $r$ is
$\bar{x} = \bar{y} = \frac{4r}{3\pi}$.
![diagram](./images/HW1019-quarter-circle.png)
Use integration to prove that the centroid of a quarter-circular area with radius $r$ is
$\bar{x} = \bar{y} = \frac{4r}{3\pi}$.