integral from 0 to 5 of (x-2)(x-4)

解

\int_{0}^{5} (x - 2) (x - 4) d x

\frac{20}{3}

十進法表記

6.66666 \dots

解答ステップ

\int_{0}^{5} (x - 2) (x - 4) d x

拡張

(x - 2) (x - 4) : x^{2} - 6 x + 8

= \int_{0}^{5} 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_{0}^{5} x^{2} d x - \int_{0}^{5} 6 x d x + \int_{0}^{5} 8 d x

\int_{0}^{5} x^{2} d x = \frac{125}{3}

\int_{0}^{5} 6 x d x = 75

\int_{0}^{5} 8 d x = 40

= \frac{125}{3} - 75 + 40

簡素化

\frac{125}{3} - 75 + 40 : \frac{20}{3}

= \frac{20}{3}