integral from 2 to 4 of-x^2+6x-8

解

\int_{2}^{4} - x^{2} + 6 x - 8 d x

\frac{4}{3}

十進法表記

1.33333 \dots

解答ステップ

\int_{2}^{4} - x^{2} + 6 x - 8 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_{2}^{4} x^{2} d x + \int_{2}^{4} 6 x d x - \int_{2}^{4} 8 d x

\int_{2}^{4} x^{2} d x = \frac{56}{3}

\int_{2}^{4} 6 x d x = 36

\int_{2}^{4} 8 d x = 16

= - \frac{56}{3} + 36 - 16

簡素化

- \frac{56}{3} + 36 - 16 : \frac{4}{3}

= \frac{4}{3}