Question

Find the area bounded by the curve $y=x(x-1)(x-2)$ and the $x$ axis.

Answer 1

Area$={\int }_0^{1}x(x-1)(x-2)dx+(-1){\int }_1^{2}x(x-1)(x-2)dx$

$=[\frac{x^4}{4}-\frac{3x^3}{3}+\frac{2x^2}{2}{]}_0^1+(-1\left)\right[\frac{x^4}{4}-\frac{3x^3}{3}+\frac{2x^2}{2}{]}_1^2$

$=\frac{1}{4}+(-1)\left(\frac{-1}{4}\right)=\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$ sq units.