integral from 2 to 4 of 4(3x-1)

解

\int_{2}^{4} 4 (3 x - 1) d x

64

解答ステップ

\int_{2}^{4} 4 (3 x - 1) d x

定数を除く:

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

= 4 \cdot \int_{2}^{4} 3 x - 1 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

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

\int_{2}^{4} 3 x d x = 18

\int_{2}^{4} 1 d x = 2

= 4 (18 - 2)

簡素化

= 64