integral from 0 to 4pi of sin(2x)

解答

\int_{0}^{4 π} sin (2 x) d x

0

求解步骤

\int_{0}^{4 π} sin (2 x) d x

使用换元积分法

= \int_{0}^{8 π} sin (u) \frac{1}{2} d u

提出常数:

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

= \frac{1}{2} \cdot \int_{0}^{8 π} sin (u) d u

使用积分常见定则:

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

= \frac{1}{2} [- cos (u)]_{0}^{8 π}

带入上下限计算后得:

0

= \frac{1}{2} \cdot 0

化简

= 0

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