integral from 0 to 6 of-3x^2-12x+180

解答

\int_{0}^{6} - 3 x^{2} - 12 x + 180 d x

648

求解步骤

\int_{0}^{6} - 3 x^{2} - 12 x + 180 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_{0}^{6} 3 x^{2} d x - \int_{0}^{6} 12 x d x + \int_{0}^{6} 180 d x

\int_{0}^{6} 3 x^{2} d x = 216

\int_{0}^{6} 12 x d x = 216

\int_{0}^{6} 180 d x = 1080

= - 216 - 216 + 1080

化简

= 648

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