Question

The area enclosed between the parabola $y^2=4ax$ and the lines x = a, x = 9a is

• A. $8a^2$
• B. $\frac{8a^2}{3}$
• C. $\frac{208a^2}{3}$
• D. $a^2$

Answer 1

The correct option is C $\frac{208a^2}{3}$

Area = $2{\int }_0^{a}2\sqrt{a}\sqrt{x}dx=4\sqrt{a}{\left[\frac{x^{\frac{3}{2}}}{\left(\frac{3}{2}\right)}\right]}_a^{9a}$
$=\left(\frac{8\sqrt{a}}{3}\right)(27a\sqrt{a}-a\sqrt{a})=\frac{208a^2}{3}$