integral from 0 to 6 of pi(6-z)

解

\int_{0}^{6} π (6 - z) d z

18 π

十進法表記

56.54866 \dots

解答ステップ

\int_{0}^{6} π (6 - z) d z

定数を除く:

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

= π \cdot \int_{0}^{6} 6 - z d z

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}^{6} 6 d z - \int_{0}^{6} z d z)

\int_{0}^{6} 6 d z = 36

\int_{0}^{6} z d z = 18

= π (36 - 18)

簡素化

= 18 π