integral from-2 to 1 of (3x^2-6x+2)

解答

\int_{- 2}^{1} (3 x^{2} - 6 x + 2) d x

24

求解步骤

\int_{- 2}^{1} 3 x^{2} - 6 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_{- 2}^{1} 3 x^{2} d x - \int_{- 2}^{1} 6 x d x + \int_{- 2}^{1} 2 d x

\int_{- 2}^{1} 3 x^{2} d x = 9

\int_{- 2}^{1} 6 x d x = - 9

\int_{- 2}^{1} 2 d x = 6

= 9 - (- 9) + 6

化简

= 24

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