integral from-2 to-1 of 2x^2-4x-6

解答

\int_{- 2}^{- 1} 2 x^{2} - 4 x - 6 d x

\frac{14}{3}

十进制

4.66666 \dots

求解步骤

\int_{- 2}^{- 1} 2 x^{2} - 4 x - 6 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} 2 x^{2} d x - \int_{- 2}^{- 1} 4 x d x - \int_{- 2}^{- 1} 6 d x

\int_{- 2}^{- 1} 2 x^{2} d x = \frac{14}{3}

\int_{- 2}^{- 1} 4 x d x = - 6

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

= \frac{14}{3} - (- 6) - 6

化简

= \frac{14}{3}

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