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integral from 0 to 1 of x(4x^4-(x^4)/4)

解答

\int_{0}^{1} x (4 x^{4} - \frac{x ^{4}}{4}) d x

解答

\frac{5}{8}

+1

十进制

0.625

求解步骤

\int_{0}^{1} x (4 x^{4} - \frac{x ^{4}}{4}) d x

化简

4 x^{4} - \frac{x ^{4}}{4} : \frac{15 x ^{4}}{4}

= \int_{0}^{1} x \frac{15 x ^{4}}{4} d x

提出常数:

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

= \frac{15}{4} \cdot \int_{0}^{1} x x^{4} d x

化简

x x^{4} : x^{5}

= \frac{15}{4} \cdot \int_{0}^{1} x^{5} d x

使用幂法则

= \frac{15}{4} [\frac{x ^{6}}{6}]_{0}^{1}

带入上下限计算后得:

\frac{1}{6}

= \frac{15}{4} \cdot \frac{1}{6}

化简

= \frac{5}{8}

作图

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