Answer
$= \frac{4}{3} $
Work Step by Step
$\int^{2}_0 2x-x^{2} dx$
$= 2\frac{x^{2}}{2} - \frac{x^{3}}{3} |^{2}_0$
$= x^{2} - \frac{x^{3}}{3} |^{2}_0$
$= [2^{2} - \frac{2^{3}}{3}] - [0^{2} - \frac{0^{3}}{3}]$
$= [4 - \frac{8}{3}] - 0$
$= [4 - \frac{8}{3}] $
$= \frac{4}{3} $