Q. The area bounded by the parabola $y^{2} = 4ax\$and the line $x = a$ and $x = 4a$ is
A) $\frac{{35a}^{2}}{3}$
B) $\frac{4a^{2}}{3}$
C) $\frac{{7a}^{2}}{3}$
D) $\frac{{56a}^{2}}{3}$
Explanation
(d)
Required area $= 2$ area of curve PSRQP
[image:8_image84.jpeg]
$= 2\int_{a}^{4a}{\sqrt{4\ ax}\ dx = 4\sqrt{a}\left\lbrack \frac{x^{3/2}}{3/2} \right\rbrack_{a}^{4a}}$
$= \frac{8}{3}\sqrt{a}\left( 8a^{\frac{3}{2}} - a^{\frac{3}{2}} \right) = \frac{{56a}^{2}}{3}\ squnits$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.