integral from 1 to 5 of pi(x-1)

解

\int_{1}^{5} π (x - 1) d x

8 π

十進法表記

25.13274 \dots

解答ステップ

\int_{1}^{5} π (x - 1) d x

定数を除く:

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

= π \cdot \int_{1}^{5} 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

= π (\int_{1}^{5} x d x - \int_{1}^{5} 1 d x)

\int_{1}^{5} x d x = 12

\int_{1}^{5} 1 d x = 4

= π (12 - 4)

簡素化

= 8 π