List of top Mathematics Questions on Area under Simple Curves asked in UP Board XII

Find the area of the region bounded by the ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1. \]
If the area bounded by the curve $x=y^{2}$ and the line $x=4$ is divided into two equal parts by the line $x=a$, find the value of $a$.