integral from 3 to 7 of ((2x-3))/6

解

\int_{3}^{7} \frac{( 2 x - 3 )}{6} d x

\frac{14}{3}

十進法表記

4.66666 \dots

解答ステップ

\int_{3}^{7} \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}^{7} 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}^{7} 2 x d x - \int_{3}^{7} 3 d x)

\int_{3}^{7} 2 x d x = 40

\int_{3}^{7} 3 d x = 12

= \frac{1}{6} (40 - 12)

簡素化

\frac{1}{6} (40 - 12) : \frac{14}{3}

= \frac{14}{3}