Area bounded by the curves y^2=9x and y=3x is :

The correct answer is Option (3) → $\frac{1}{2}sq\, units$

$y^2=9x$, $y=3x$

they interact at $(3x)^2=9x$

so $x^2=x, x=0,1$

$y=0,3$

Area required = $\int\limits_0^13\sqrt{x}-3xdx$

$=\left[\frac{2}{3}x^{\frac{3}{2}}-\frac{x^2}{2}\right]_0^1=\frac{1}{2}$ sq. units