AIEEE 2012 (Offline) 29th April Code AQuestion 1
The area bounded between the parabolas $x^2=\frac y4$ and $x^2=9y$, and the straight line $y=2$ is :
Application of Integrals
Solution
$x^2=y/4\Rightarrow x=\pm\frac{\sqrt y}{2}$ and $x^2=9y\Rightarrow x=\pm3\sqrt y$. Area $=2\int_0^2\left(3-\frac12\right)\sqrt y\,dy=5\cdot\frac23\cdot2\sqrt2=\frac{20\sqrt2}{3}$.