integral from 0 to pi of 1cos(n)x

解答

\int_{0}^{π} 1 cos (n) x d x

cos (n) \frac{π ^{2}}{2}

求解步骤

\int_{0}^{π} 1 \cdot cos (n) x d x

提出常数:

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

= 1 \cdot cos (n) \cdot \int_{0}^{π} x d x

化简

= cos (n) \cdot \int_{0}^{π} x d x

使用幂法则

= cos (n) [\frac{x ^{2}}{2}]_{0}^{π}

带入上下限计算后得:

\frac{π ^{2}}{2}

= cos (n) \frac{π ^{2}}{2}

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