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

解

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

10

解答ステップ

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

定数を除く:

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

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

\int_{2}^{6} 2 x d x = 32

\int_{2}^{6} 3 d x = 12

= \frac{1}{2} (32 - 12)

簡素化

\frac{1}{2} (32 - 12) : 10

= 10