question_answer

The area bounded by the parabola \[{{y}^{2}}=4ax,\] its axis and two ordinates \[x=4,\] \[x=9\] is

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

B)            \[4{{a}^{2}}.4\]

C)            \[4{{a}^{2}}(9-4)\]             

D)            \[\frac{152\sqrt{a}}{3}\]

Correct Answer: D

Solution :

                   Shaded area \[A=2\int_{4}^{9}{\sqrt{4ax}dx}\]            \[A=4\sqrt{a}\times \frac{2}{3}[{{x}^{3/2}}]_{4}^{9}=\frac{152\sqrt{a}}{3}\].