integral from-3 to 3 of (x+2)(x-2)

解答

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

- 6

求解步骤

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

乘开

(x + 2) (x - 2) : x^{2} - 4

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

\int_{- 3}^{3} x^{2} d x = 18

\int_{- 3}^{3} 4 d x = 24

= 18 - 24

化简

= - 6

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