A circular corral with a radius of 11 is enclosed by a fence. A goat inside the corral is tied to the fence with a rope of length $0 \le a \le 22$ (see figure to the right). What is the area of the region (inside the corral) that the goat can graze? Check your answer with the special cases $a=0$ and $a=22$.
Let the point where the goat is tied to the fence represent the origin and point $(0,11)$ be the center of the corral in Cartesian coordinates. Set up the integral(s) that give(s) the area of the region. Select the correct choice below and fill in the answer box(es) to complete your choice.
A. $\int_{0}^{\sin^{-1}(a/22)} (\quad) d\theta$
B. $\int_{0}^{\sin^{-1}(a/22)} (\quad) d\theta + \int_{\sin^{-1}(a/22)}^{\pi} (\quad) d\theta$
C. $\int_{0}^{\sin^{-1}(a/22)} (\quad) d\theta + \int_{\sin^{-1}(a/22)}^{\pi/2} (\quad) d\theta$
