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

解答

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

\frac{31}{6}

十进制

5.16666 \dots

求解步骤

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

\int_{1}^{2} 2 x^{3} d x = \frac{15}{2}

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

= \frac{15}{2} - \frac{7}{3}

化简

\frac{15}{2} - \frac{7}{3} : \frac{31}{6}

= \frac{31}{6}

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