integral from 0 to 4 of (x-3)(x-5)

解

\int_{0}^{4} (x - 3) (x - 5) d x

\frac{52}{3}

十進法表記

17.33333 \dots

解答ステップ

\int_{0}^{4} (x - 3) (x - 5) d x

拡張

(x - 3) (x - 5) : x^{2} - 8 x + 15

= \int_{0}^{4} x^{2} - 8 x + 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_{0}^{4} x^{2} d x - \int_{0}^{4} 8 x d x + \int_{0}^{4} 15 d x

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 8 x d x = 64

\int_{0}^{4} 15 d x = 60

= \frac{64}{3} - 64 + 60

簡素化

\frac{64}{3} - 64 + 60 : \frac{52}{3}

= \frac{52}{3}