integral from 3 to 6 of x^2-6x+9

解答

\int_{3}^{6} x^{2} - 6 x + 9 d x

9

求解步骤

\int_{3}^{6} x^{2} - 6 x + 9 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}^{6} x^{2} d x - \int_{3}^{6} 6 x d x + \int_{3}^{6} 9 d x

\int_{3}^{6} x^{2} d x = 63

\int_{3}^{6} 6 x d x = 81

\int_{3}^{6} 9 d x = 27

= 63 - 81 + 27

化简

= 9

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