\displaystyle \int_{0}^{4}(u-2u^{\frac{1}{2}})\,du = \left[\frac12 u^{2}-2\cdot \frac23 u^{\frac{3}{2}}\right]_{0}^{4} = \left[\frac12 u^{2}-\frac43 u^{\frac{3}{2}}\right]_{0}^{4}

\displaystyle =\left(\frac12(16)-\frac43(4^{\frac{3}{2}})\right)-(0) =8-\frac43(8) =8-\frac{32}{3} =\frac{24-32}{3} =-\frac{8}{3}이다.