What is the area of the part of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ that lies in the first quadrant?

Explanation

1. 01

   $\int_0^{a} \frac{b}{a}\sqrt{a^{2} - x^{2}}\,dx = \frac{b}{a} \cdot \frac{\pi a^{2}}{4}$.

2. 02

   $= \frac{\pi ab}{4}$, a quarter of the whole ellipse.