question_answer

The area bounded by the curves \[{{y}^{2}}=4x\]and \[{{x}^{2}}=4y\]is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A) \[\frac{32}{3}\]

B) \[\frac{16}{3}\]

C) \[\frac{8}{3}\]

D)  0

Correct Answer: B

Solution :

    Area\[=\int\limits_{0}^{4}{\left( 2\sqrt{x}-\frac{{{x}^{2}}}{4} \right)dx}\] \[=\left( 2\left( \frac{{{x}^{3/2}}}{3/2} \right)-\frac{{{x}^{3}}}{12} \right)_{0}^{4}\] \[=\frac{4}{3}\times 8-\frac{64}{12}\] \[=\frac{32}{3}-\frac{16}{3}=\frac{16}{3}\]