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

解

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

1

解答ステップ

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

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{1}^{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

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

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

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

= 2 (\frac{3}{2} - 1)

簡素化

2 (\frac{3}{2} - 1) : 1

= 1