integral from 2 to 6 of 1/5 x^2

解答

\int_{2}^{6} \frac{1}{5} x^{2} d x

\frac{208}{15}

十进制

13.86666 \dots

求解步骤

\int_{2}^{6} \frac{1}{5} x^{2} d x

提出常数:

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

= \frac{1}{5} \cdot \int_{2}^{6} x^{2} d x

使用幂法则

= \frac{1}{5} [\frac{x ^{3}}{3}]_{2}^{6}

带入上下限计算后得:

\frac{208}{3}

= \frac{1}{5} \cdot \frac{208}{3}

化简

= \frac{208}{15}

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