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

解

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

\frac{1}{3}

十進法表記

0.33333 \dots

解答ステップ

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

拡張

(x - 1)^{2} : x^{2} - 2 x + 1

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

\int_{1}^{2} x^{2} d x = \frac{7}{3}

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

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

= \frac{7}{3} - 3 + 1

簡素化

\frac{7}{3} - 3 + 1 : \frac{1}{3}

= \frac{1}{3}