Question

The area bounded between the parabolas $x^2=\frac{y}{4}$ and $x^2=9y$ and the straight line $y=2$ is :

• A. $20\sqrt{2}$
• B. $\frac{10\sqrt{2}}{3}$
• C. $\frac{20\sqrt{2}}{3}$
• D. $10\sqrt{2}$

Answer 1

Answer: (C)

$y=4x^2$
$y=\frac{1}{9}{x}^2$
Area $=2{\int }_0^2\left(3\sqrt{y}-\frac{\sqrt{y}}{2}\right)dy=2{\left[\frac{5}{2}\frac{y\sqrt{y}}{3/2}\right]}_0^2=2.\frac{5}{3}2\sqrt{2}=\frac{20\sqrt{2}}{3}$