정적분 계산

함수 $f \left( x \right) = x ^{2} + x$에 대하여 $\displaystyle 5 \int _{0} ^{1} {} f \left( x \right) dx - \int _{0} ^{1} {} \left( 5 x + f \left( x \right) \right) dx$ $\displaystyle = \int _{0} ^{1} {} \left\{ 5 f \left( x \right) - \left( 5 x + f \left( x \right) \right) \right\} dx$ $\displaystyle = \int _{0} ^{1} {} \left( 4 f \left( x \right) - 5 x \right) dx$ $\displaystyle = \int _{0} ^{1} {} \left( 4 x ^{2} - x \right) dx$ $\displaystyle = \left[ \begin{array}{l} \begin{matrix} \\ \end{matrix} \frac{4}{3} x ^{3} - \frac{1}{2} x ^{2} \end{array} \right] _{0} ^{1}$ $\displaystyle = \frac{5}{6}$