integral from 0 to pi of xcos(n)x

解答

\int_{0}^{π} x cos (n) x d x

cos (n) \frac{π ^{3}}{3}

求解步骤

\int_{0}^{π} x cos (n) x d x

提出常数:

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

= cos (n) \cdot \int_{0}^{π} xx d x

化简

xx : x^{2}

= cos (n) \cdot \int_{0}^{π} x^{2} d x

使用幂法则

= cos (n) [\frac{x ^{3}}{3}]_{0}^{π}

带入上下限计算后得:

\frac{π ^{3}}{3}

= cos (n) \frac{π ^{3}}{3}

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