integral from 0 to pi of asin(x)

解答

\int_{0}^{π} a sin (x) d x

a \cdot 2

求解步骤

\int_{0}^{π} a sin (x) d x

提出常数:

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

= a \cdot \int_{0}^{π} sin (x) d x

使用积分常见定则:

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

= a [- cos (x)]_{0}^{π}

带入上下限计算后得:

2

= a \cdot 2

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