question_answer

The area bounded by curve \[{{y}^{2}}=x,\] line \[y=4\] and y-axis is                          [Roorkee 1995; RPET 2003]

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

B)            \[\frac{64}{3}\]

C)            \[7\sqrt{2}\]                         

D)            None of these

Correct Answer: B

Solution :

                   Required area = area of OABC ? area of OBC                                       \[=16\times 4-\int_{0}^{16}{\sqrt{x}}dx=64-\left[ \frac{{{x}^{3/2}}}{3/2} \right]_{0}^{16}=\frac{64}{3}.\]