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

解

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

\frac{3}{10}

十進法表記

0.3

解答ステップ

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

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

\int_{1}^{2} 1 d x = 1

\int_{1}^{2} (x - 1)^{4} d x = \frac{1}{5}

= \frac{3}{2} - 1 - \frac{1}{5}

簡素化

\frac{3}{2} - 1 - \frac{1}{5} : \frac{3}{10}

= \frac{3}{10}