question_answer

The area bounded between the parabolas \[{{x}^{2}}=\frac{y}{4}\] and \[{{x}^{2}}=9y\] and the straight line \[y=2\]is:   AIEEE  Solved  Paper-2012

A) \[20\sqrt{2}\]                       

B) \[\frac{10\sqrt{2}}{3}\]

C) \[\frac{20\sqrt{2}}{3}\]                    

D) \[10\sqrt{2}\]

Correct Answer: C

Solution :

                     \[y=4{{x}^{2}}\] \[y=\frac{1}{9}{{x}^{2}}\] Area \[=2\int\limits_{0}^{2}{\left( 3\sqrt{y}-\frac{\sqrt{y}}{2} \right)dy=2}\left[ \frac{5}{2}\frac{y\sqrt{y}}{3/2} \right]_{0}^{2}\] \[=2.\frac{5}{3}2\sqrt{2}=\frac{20\sqrt{2}}{3}\]