integral from-2 to-1 of (4x^3+2/(x^3))

解答

\int_{- 2}^{- 1} (4 x^{3} + \frac{2}{x ^{3}}) d x

- \frac{63}{4}

十进制

- 15.75

求解步骤

\int_{- 2}^{- 1} 4 x^{3} + \frac{2}{x ^{3}} 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_{- 2}^{- 1} 4 x^{3} d x + \int_{- 2}^{- 1} \frac{2}{x ^{3}} d x

\int_{- 2}^{- 1} 4 x^{3} d x = - 15

\int_{- 2}^{- 1} \frac{2}{x ^{3}} d x = - \frac{3}{4}

= - 15 - \frac{3}{4}

化简

- 15 - \frac{3}{4} : - \frac{63}{4}

= - \frac{63}{4}

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