Question

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

Answer 1

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

$x=2x-x^2$

$x=0,1$

The area enclosed between x=1 and x=4 is ${\int }_0^1(2x-x^2-x)dx$

$=[\frac{x^2}{2}-\frac{x^3}{3}{]}_0^1=\frac{1}{6}$