integral from 0 to 2 of pi^8x

解答

\int_{0}^{2} π^{8} x d x

π^{8} \cdot 2

十进制

18977.06203 \dots

求解步骤

\int_{0}^{2} π^{8} x d x

提出常数:

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

= π^{8} \cdot \int_{0}^{2} x d x

使用幂法则

= π^{8} [\frac{x ^{2}}{2}]_{0}^{2}

带入上下限计算后得:

2

= π^{8} \cdot 2

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