Given curves are y2 = 9x and y = 3x
solving the two equations we have
![\[\begin{array}{*{35}{l}} {{\left( 3x \right)}^{2}}~=\text{ }9x \\ 9{{x}^{2}}~=\text{ }9x \\ 9{{x}^{2}}~\text{ }-9x\text{ }=\text{ }0\text{ }\Rightarrow \text{ }9x\left( x\text{ }-\text{ }1 \right)\text{ }=\text{ }0 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5701b765ca19d2eb2ec3e6c61e9a83d5_l3.png "Rendered by QuickLaTeX.com")
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.
Find the area of the region bounded by the curves y^2 = 9x, y = 3x.
Find the area of the region bounded by the curves y^2 = 9x, y = 3x.