integral from-4 to-1 of (-2x^2-12x-12)

解答

\int_{- 4}^{- 1} (- 2 x^{2} - 12 x - 12) d x

12

求解步骤

\int_{- 4}^{- 1} - 2 x^{2} - 12 x - 12 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_{- 4}^{- 1} 2 x^{2} d x - \int_{- 4}^{- 1} 12 x d x - \int_{- 4}^{- 1} 12 d x

\int_{- 4}^{- 1} 2 x^{2} d x = 42

\int_{- 4}^{- 1} 12 x d x = - 90

\int_{- 4}^{- 1} 12 d x = 36

= - 42 - (- 90) - 36

化简

= 12

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