integral from-1 to 1 of (x^4-x^8)

解答

\int_{- 1}^{1} (x^{4} - x^{8}) d x

\frac{8}{45}

十进制

0.17777 \dots

求解步骤

\int_{- 1}^{1} x^{4} - x^{8} 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}^{1} x^{4} d x - \int_{- 1}^{1} x^{8} d x

\int_{- 1}^{1} x^{4} d x = \frac{2}{5}

\int_{- 1}^{1} x^{8} d x = \frac{2}{9}

= \frac{2}{5} - \frac{2}{9}

化简

\frac{2}{5} - \frac{2}{9} : \frac{8}{45}

= \frac{8}{45}

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