question_answer

The area between the curve \[{{y}^{2}}=4ax,\] x-axis and the ordinates \[x=0\] and \[x=a\] is                                    [RPET 1996]

A)            \[\frac{4}{3}{{a}^{2}}\]    

B)            \[\frac{8}{3}{{a}^{2}}\]

C)            \[\frac{2}{3}{{a}^{2}}\]    

D)            \[\frac{5}{3}{{a}^{2}}\]

Correct Answer: B

Solution :

           Required area \[=2\int_{0}^{a}{\sqrt{4ax}dx}\]            \[=4\sqrt{a}\times \frac{2}{3}[{{x}^{3/2}}]_{0}^{a}=\frac{8\sqrt{a}}{3}.a\sqrt{a}=\frac{8}{3}{{a}^{2}}\].