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. $40\sqrt{2}$

Answer 1

The correct option is C $\frac{20\sqrt{2}}{3}$


Required area
$=2\underset{0}{\overset{2}{\int }}(3\sqrt{y}-\frac{\sqrt{y}}{2})dy$
$=2{[\frac{5}{2}\times \frac{2}{3}{y}^{3/2}]}_0^2$
$=\frac{20\sqrt{2}}{3}$