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

解

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

- \frac{125}{6}

十進法表記

- 20.83333 \dots

解答ステップ

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

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

\int_{- 5}^{0} 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}