Question

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

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

Answer 1

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

$y^2=4ax$
$2\stackrel{9a}{\underset{a}{\int }}\sqrt{4ax}dx$
$\frac{2}{3}\times 4\stackrel{9a}{\underset{a}{\int }}\sqrt{a}{x}^{3/2}$
$=8/3\left[\right(27a^2-a^2\left)\right]$
$=\frac{208a^2}{3}$