Question

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

Answer 1

Given the curves $y=x^2,y=2x-x^2$

$x^2=2x-x^2$

$x=0,1$

The area enclosed between the curve , x=0 and x=1 is ${\int }_0^1(2x-x^2-x^2)dx$

$={\int }_0^1(2x-2x^2)dx=[x^2-2\frac{x^3}{3}{]}_0^1=\frac{1}{3}sq.units$