integral from 0 to 10 of 9800pi(10-y)

解答

\int_{0}^{10} 9800 π (10 - y) d y

490000 π

十进制

1539380.40025 \dots

求解步骤

\int_{0}^{10} 9800 π (10 - y) d y

提出常数:

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

= 9800 π \cdot \int_{0}^{10} 10 - y d y

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 9800 π (\int_{0}^{10} 10 d y - \int_{0}^{10} y d y)

\int_{0}^{10} 10 d y = 100

\int_{0}^{10} y d y = 50

= 9800 π (100 - 50)

化简

= 490000 π

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