integral from-1 to 1 of-4x^5+3x-2

解答

\int_{- 1}^{1} - 4 x^{5} + 3 x - 2 d x

- 4

求解步骤

\int_{- 1}^{1} - 4 x^{5} + 3 x - 2 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} 4 x^{5} d x + \int_{- 1}^{1} 3 x d x - \int_{- 1}^{1} 2 d x

\int_{- 1}^{1} 4 x^{5} d x = 0

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

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

= - 0 + 0 - 4

化简

= - 4

\int_{0}^{4} 6 x e^{3 x^{2}} d x

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