integral from 0 to 5 of (7x-x^2)-2x

解

\int_{0}^{5} (7 x - x^{2}) - 2 x d x

\frac{125}{6}

十進法表記

20.83333 \dots

解答ステップ

\int_{0}^{5} 7 x - x^{2} - 2 x d x

簡素化

= \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}