integral from 0 to 2 of x(x^2-1)

解答

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

2

求解步骤

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

乘开

x (x^{2} - 1) : x^{3} - x

= \int_{0}^{2} x^{3} - 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_{0}^{2} x^{3} d x - \int_{0}^{2} x d x

\int_{0}^{2} x^{3} d x = 4

\int_{0}^{2} x d x = 2

= 4 - 2

化简

= 2

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