Question

Find the area of the closed figure bounded by the following curves y=x(x-3) and the x axis.

Answer 1

First we make a rough shetch of the curve $y=x(x-3)$.

In this case the required area $o$ below $x$ axis.

Using $A=\int ydx$ and substituting $y$ from equation of the curve we cannot integrate $y$ with respect to $x$.

$A={\int }_0^{3}x(x-3)dx$

$={[\frac{x^3}{3}-\frac{{3x}^2}{2}]}_0^3$

$=(9-\frac{27}{2})-0$

$=-4\frac{1}{2}$

So negative sign excluded numerical value is $4\frac{1}{2}$.