integral from 0 to pi of (10sin(x))

解答

\int_{0}^{π} (10 sin (x)) d x

20

求解步骤

\int_{0}^{π} 10 sin (x) d x

提出常数:

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

= 10 \cdot \int_{0}^{π} sin (x) d x

使用积分常见定则:

\int sin (x) d x = - cos (x)

= 10 [- cos (x)]_{0}^{π}

带入上下限计算后得:

2

= 10 \cdot 2

化简

= 20

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