Question

Find the area of the closed figure bounded by the following curves:
$y$ = $2x-x^2$, $y=0.$

Answer 1

$y=2x-x^2,y=0$

${\int }_0^{2}ydx={\int }_0^{2}2x-x^{2}dx$

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

$=4-\frac{8}{3}=\frac{12-8}{3}$

$=\frac{4}{3}$ (required area).