What is the area of the region bounded by the curve $x = \sqrt{25 - y^{2}}$ and the $y$-axis?

Explanation

1. 01

   $x = \sqrt{25 - y^{2}}$ is the right half of the circle $x^{2} + y^{2} = 25$, from $y = -5$ to $y = 5$.

2. 02

   Horizontal strips: $\int_{-5}^{5} \sqrt{25 - y^{2}}\,dy = \frac{25\pi}{2}$ square units, half the circle.