integral from 7 to 10 of (7-x)(x-10)

解

\int_{7}^{10} (7 - x) (x - 10) d x

\frac{9}{2}

十進法表記

4.5

解答ステップ

\int_{7}^{10} (7 - x) (x - 10) d x

拡張

(7 - x) (x - 10) : 17 x - x^{2} - 70

= \int_{7}^{10} 17 x - x^{2} - 70 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_{7}^{10} 17 x d x - \int_{7}^{10} x^{2} d x - \int_{7}^{10} 70 d x

\int_{7}^{10} 17 x d x = \frac{867}{2}

\int_{7}^{10} x^{2} d x = 219

\int_{7}^{10} 70 d x = 210

= \frac{867}{2} - 219 - 210

簡素化

\frac{867}{2} - 219 - 210 : \frac{9}{2}

= \frac{9}{2}