integral from 0 to 1 of (5x^2-8x+5)

解

\int_{0}^{1} (5 x^{2} - 8 x + 5) d x

\frac{8}{3}

十進法表記

2.66666 \dots

解答ステップ

\int_{0}^{1} 5 x^{2} - 8 x + 5 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}^{1} 5 x^{2} d x - \int_{0}^{1} 8 x d x + \int_{0}^{1} 5 d x

\int_{0}^{1} 5 x^{2} d x = \frac{5}{3}

\int_{0}^{1} 8 x d x = 4

\int_{0}^{1} 5 d x = 5

= \frac{5}{3} - 4 + 5

簡素化

\frac{5}{3} - 4 + 5 : \frac{8}{3}

= \frac{8}{3}