integral from 1 to 2 of 3x-x^2+2

解答

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

\frac{25}{6}

十进制

4.16666 \dots

求解步骤

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

\int_{1}^{2} 3 x d x = \frac{9}{2}

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

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

= \frac{9}{2} - \frac{7}{3} + 2

化简

\frac{9}{2} - \frac{7}{3} + 2 : \frac{25}{6}

= \frac{25}{6}

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