Using integration, what is the area enclosed by the circle $x^{2} + y^{2} = 25$?

Explanation

1. 01

   By symmetry, 4 times the quadrant: $4\int_0^{5} \sqrt{25 - x^{2}}\,dx$.

2. 02

   The quadrant is $\frac{25\pi}{4}$, so the area is $25\pi$ square units.