Answer
$\frac{4569}{80}$
Work Step by Step
$\int^{-1}_{-8} \frac{x-x^2}{2\sqrt[3] x} dx$
$\frac{1}{2}\int^{-1}_{-8} (x^{\frac{2}{3}}-x^{\frac{5}{3}})dx$, Rewrite
$\frac{1}{2}(\frac{3}{5}x^{\frac{5}{3}} - \frac{3}{8}x^{\frac{8}{3}})]^{-1}_{-8}$, Integrate
$\frac{1}{2}[(\frac{-24-15}{40}) - (\frac{-768-3840}{40})]$, Take Definite Integral
$\frac{4569}{80}$, Simplify
