integral from 0 to 4 of pi(4-y)

解

\int_{0}^{4} π (4 - y) d y

8 π

十進法表記

25.13274 \dots

解答ステップ

\int_{0}^{4} π (4 - y) d y

定数を除く:

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

= π \cdot \int_{0}^{4} 4 - y d y

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_{0}^{4} 4 d y - \int_{0}^{4} y d y)

\int_{0}^{4} 4 d y = 16

\int_{0}^{4} y d y = 8

= π (16 - 8)

簡素化

= 8 π