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

解

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

3

解答ステップ

\int_{3}^{6} \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_{3}^{6} 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_{3}^{6} 2 x d x - \int_{3}^{6} 3 d x)

\int_{3}^{6} 2 x d x = 27

\int_{3}^{6} 3 d x = 9

= \frac{1}{6} (27 - 9)

簡素化

\frac{1}{6} (27 - 9) : 3

= 3