integral from 1 to 7 of (-1/3 x^2+3x)

解答

\int_{1}^{7} (- \frac{1}{3} x^{2} + 3 x) d x

34

求解步骤

\int_{1}^{7} - \frac{1}{3} x^{2} + 3 x 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_{1}^{7} \frac{1}{3} x^{2} d x + \int_{1}^{7} 3 x d x

\int_{1}^{7} \frac{1}{3} x^{2} d x = 38

\int_{1}^{7} 3 x d x = 72

= - 38 + 72

化简

= 34

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