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

解答

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

\frac{55}{64}

十进制

0.859375

求解步骤

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

\int_{- \frac{3}{2}}^{1} x^{3} d x = - \frac{65}{64}

\int_{- \frac{3}{2}}^{1} 3 x d x = - \frac{15}{8}

= - \frac{65}{64} - (- \frac{15}{8})

化简

- \frac{65}{64} - (- \frac{15}{8}) : \frac{55}{64}

= \frac{55}{64}

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