Answer
$\frac{16\sqrt 2}{15} $
Work Step by Step
$\int^2_0 (2-t)\sqrt t dt $
$\int^2_0 (2t^{\frac{1}{2}} - t^{\frac{3}{2}})dt$, Rewrite
$\frac{4}{3}t^{\frac{3}{2}}-\frac{2}{5}t^{\frac{5}{2}} $, Integrate
${\frac{4}{3}t^{\frac{3}{2}}-\frac{2}{5}t^{\frac{5}{2}}}]^2_0 $, Definite Integral Form
$(\frac{8}{3}\sqrt 2 - \frac{8}{5}\sqrt 2)$, Take Definite Integral
$\frac{16\sqrt 2}{15}$, Simplify
