integral from 2 to 4 of ((2x-3))/6

解

\int_{2}^{4} \frac{( 2 x - 3 )}{6} d x

1

解答ステップ

\int_{2}^{4} \frac{2 x - 3}{6} d x

定数を除く:

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

= \frac{1}{6} \cdot \int_{2}^{4} 2 x - 3 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{1}{6} (\int_{2}^{4} 2 x d x - \int_{2}^{4} 3 d x)

\int_{2}^{4} 2 x d x = 12

\int_{2}^{4} 3 d x = 6

= \frac{1}{6} (12 - 6)

簡素化

\frac{1}{6} (12 - 6) : 1

= 1