integral from pi/2 to pi of cos(2θ)

解答

\int_{\frac{π}{2}}^{π} cos (2 θ) d θ

0

求解步骤

\int_{\frac{π}{2}}^{π} cos (2 θ) d θ

使用换元积分法

= \int_{π}^{2 π} cos (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_{π}^{2 π} cos (u) d u

使用积分常见定则:

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

= \frac{1}{2} [sin (u)]_{π}^{2 π}

带入上下限计算后得:

0

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

化简

= 0

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