integral from 5 to 7 of x^2+x+1-15

解

\int_{5}^{7} x^{2} + x + 1 - 15 d x

\frac{170}{3}

十進法表記

56.66666 \dots

解答ステップ

\int_{5}^{7} x^{2} + x + 1 - 15 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}^{7} x^{2} d x + \int_{5}^{7} x d x + \int_{5}^{7} 1 d x - \int_{5}^{7} 15 d x

\int_{5}^{7} x^{2} d x = \frac{218}{3}

\int_{5}^{7} x d x = 12

\int_{5}^{7} 1 d x = 2

\int_{5}^{7} 15 d x = 30

= \frac{218}{3} + 12 + 2 - 30

簡素化

\frac{218}{3} + 12 + 2 - 30 : \frac{170}{3}

= \frac{170}{3}