integral from 0 to 5 of 9800pi(5-y)

解

\int_{0}^{5} 9800 π (5 - y) d y

122500 π

十進法表記

384845.10006 \dots

解答ステップ

\int_{0}^{5} 9800 π (5 - y) d y

定数を除く:

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

= 9800 π \cdot \int_{0}^{5} 5 - 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

= 9800 π (\int_{0}^{5} 5 d y - \int_{0}^{5} y d y)

\int_{0}^{5} 5 d y = 25

\int_{0}^{5} y d y = \frac{25}{2}

= 9800 π (25 - \frac{25}{2})

簡素化

9800 π (25 - \frac{25}{2}) : 122500 π

= 122500 π