What is the area of the part of the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$ in the first quadrant?

Explanation

1. 01

   $y = \frac{3}{2}\sqrt{4 - x^{2}}$, so the quadrant is $\frac{3}{2}\int_0^{2} \sqrt{4 - x^{2}}\,dx = \frac{3}{2} \times \pi$.

2. 02

   $\frac{3\pi}{2}$ square units, a quarter of $\pi \times 2 \times 3$.