integral from-1 to 1 of x^3-1

解答

\int_{- 1}^{1} x^{3} - 1 d x

- 2

求解步骤

\int_{- 1}^{1} x^{3} - 1 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^{3} d x - \int_{- 1}^{1} 1 d x

\int_{- 1}^{1} x^{3} d x = 0

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

= 0 - 2

化简

= - 2

\int_{x}^{- 1} t^{2} + 1 d t

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\int_{0}^{1} (x - x^{2}) x d x