integral from 0 to 5 of (x^2-5x)

解

\int_{0}^{5} (x^{2} - 5 x) d x

- \frac{125}{6}

十進法表記

- 20.83333 \dots

解答ステップ

\int_{0}^{5} x^{2} - 5 x d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{5} x^{2} d x - \int_{0}^{5} 5 x d x

\int_{0}^{5} x^{2} d x = \frac{125}{3}

\int_{0}^{5} 5 x d x = \frac{125}{2}

= \frac{125}{3} - \frac{125}{2}

簡素化

\frac{125}{3} - \frac{125}{2} : - \frac{125}{6}

= - \frac{125}{6}