Question

Find the area of the region bounded by the curve $y=2x-x^2$ and X-axis.

Answer 1

Given $y=2x-x^2,x-axis$

the points x-axis cuts the curves are

$0=2x-x^2=x(2-x)$

$x=0orx=2$

so the points are

$A=(0,0)$ , $B=(2,0)$

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

$={[x^2-\frac{x^3}{3}]}_0^2=2^2-\frac{2^3}{3}-0=4-\frac{8}{3}$

$=\frac{4}{3}$

$\therefore$ Area$=\frac{4}{3}squnits$