integral from-1 to 0 of x^{1/5}-x

解答

\int_{- 1}^{0} x^{\frac{1}{5}} - x d x

- \frac{1}{3}

十进制

- 0.33333 \dots

求解步骤

\int_{- 1}^{0} x^{\frac{1}{5}} - x d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 1}^{0} x^{\frac{1}{5}} d x - \int_{- 1}^{0} x d x

\int_{- 1}^{0} x^{\frac{1}{5}} d x = \frac{5 ( - 1 ) ^{\frac{1}{5}}}{6}

\int_{- 1}^{0} x d x = - \frac{1}{2}

= \frac{5 ( - 1 ) ^{\frac{1}{5}}}{6} - (- \frac{1}{2})

化简

\frac{5 ( - 1 ) ^{\frac{1}{5}}}{6} - (- \frac{1}{2}) : - \frac{1}{3}

= - \frac{1}{3}

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