integral from 4 to 6 of (x^2+2x-7)

解

\int_{4}^{6} (x^{2} + 2 x - 7) d x

\frac{170}{3}

十進法表記

56.66666 \dots

解答ステップ

\int_{4}^{6} x^{2} + 2 x - 7 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_{4}^{6} x^{2} d x + \int_{4}^{6} 2 x d x - \int_{4}^{6} 7 d x

\int_{4}^{6} x^{2} d x = \frac{152}{3}

\int_{4}^{6} 2 x d x = 20

\int_{4}^{6} 7 d x = 14

= \frac{152}{3} + 20 - 14

簡素化

\frac{152}{3} + 20 - 14 : \frac{170}{3}

= \frac{170}{3}