Semicircular disk ($\{(x,y):x^2+y^2\le a^2,y\ge 0\}$)

A semicircular disk is one half of a disk cut along a diameter, including its interior. It is a circular sector of angle $\pi$, with area $\pi a^2/2$. Source polar coordinates use $0\le r\le a$, $0\le \theta \le \pi$, and area element $rdrd\theta$. Its boundary consists of a semicircle and a diameter; the semicircle alone is a curve and has no planar interior.