The area bounded by y = 3x and $y=x^2$ is

$y=3x$

$y=x^2$

Required area$={\displaystyle \underset{0}{\overset{3}{\int }}\left(3x-x^2\right)dx}$

                          $=\frac{9}{2}=4.5$

                    (OR)

(The area of bounded region bounded by $x^2=4ay$ and $y=mx$ is $\frac{8}{3}{a}^2.n^3$ sq.units )

$R.A=\frac{8}{3}{a}^2.n^3$         

    $=\frac{8}{3}{\left(\frac{1}{4}\right)}^2{3}^3$

     $=4.5$