Question

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. $\frac{56a^2}{3}$

Answer 1

Answer: (D)

$\frac{56a^2}{3}$

Required area $=$ area of curve PSMNRQP

$=2$ area of curve PSRQP

$=2{\int }_a^{4a}\sqrt{4ax}dx$

$=4\sqrt{a}{\left[\frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]}_a^{4a}=\frac{8}{3}\sqrt{a}\left[\right(4a{)}^{\frac{3}{2}}-a^{\frac{3}{2}}]$

$=\frac{8}{3}\sqrt{a}[8a^{\frac{3}{2}}-a^{\frac{3}{2}})=\frac{56}{3}{a}^2$