integral from 0 to 1 of (2(x+2))/5

解

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

1

解答ステップ

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

定数を除く:

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

= \frac{2}{5} \cdot \int_{0}^{1} x + 2 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

= \frac{2}{5} (\int_{0}^{1} x d x + \int_{0}^{1} 2 d x)

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

\int_{0}^{1} 2 d x = 2

= \frac{2}{5} (\frac{1}{2} + 2)

簡素化

\frac{2}{5} (\frac{1}{2} + 2) : 1

= 1