integral from 1 to 32 of 6/5 x^{1/5}

解答

\int_{1}^{32} \frac{6}{5} x^{\frac{1}{5}} d x

63

求解步骤

\int_{1}^{32} \frac{6}{5} x^{\frac{1}{5}} d x

提出常数:

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

= \frac{6}{5} \cdot \int_{1}^{32} x^{\frac{1}{5}} d x

使用幂法则

= \frac{6}{5} [\frac{5}{6} x^{\frac{6}{5}}]_{1}^{32}

带入上下限计算后得:

\frac{105}{2}

= \frac{6}{5} \cdot \frac{105}{2}

化简

= 63

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