integral from 1 to 8 of (x^2-4x+6)

解

\int_{1}^{8} (x^{2} - 4 x + 6) d x

\frac{259}{3}

十進法表記

86.33333 \dots

解答ステップ

\int_{1}^{8} x^{2} - 4 x + 6 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_{1}^{8} x^{2} d x - \int_{1}^{8} 4 x d x + \int_{1}^{8} 6 d x

\int_{1}^{8} x^{2} d x = \frac{511}{3}

\int_{1}^{8} 4 x d x = 126

\int_{1}^{8} 6 d x = 42

= \frac{511}{3} - 126 + 42

簡素化

\frac{511}{3} - 126 + 42 : \frac{259}{3}

= \frac{259}{3}