Find the area of the region bounded by the curves y^2 = 9x, y = 3x.

Given curves are y² = 9x and y = 3x

solving the two equations we have

\[\begin{array}{*{35}{l}}

{{\left( 3x \right)}^{2}}~=\text{ }9x  \\

9{{x}^{2}}~=\text{ }9x  \\

9{{x}^{2}}~\text{ }-9x\text{ }=\text{ }0\text{ }\Rightarrow \text{ }9x\left( x\text{ }-\text{ }1 \right)\text{ }=\text{ }0  \\

\end{array}\]

Thus, x = 0, 1

So, the area of the shaded region is given by

= ar(region OAB) – ar (Δ OAB)

Therefore, the required area is ½ sq.units.