integral from-1 to 2 of (x^3-2x^2-5x+6)

解答

\int_{- 1}^{2} (x^{3} - 2 x^{2} - 5 x + 6) d x

\frac{33}{4}

十进制

8.25

求解步骤

\int_{- 1}^{2} x^{3} - 2 x^{2} - 5 x + 6 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} x^{3} d x - \int_{- 1}^{2} 2 x^{2} d x - \int_{- 1}^{2} 5 x d x + \int_{- 1}^{2} 6 d x

\int_{- 1}^{2} x^{3} d x = \frac{15}{4}

\int_{- 1}^{2} 2 x^{2} d x = 6

\int_{- 1}^{2} 5 x d x = \frac{15}{2}

\int_{- 1}^{2} 6 d x = 18

= \frac{15}{4} - 6 - \frac{15}{2} + 18

化简

\frac{15}{4} - 6 - \frac{15}{2} + 18 : \frac{33}{4}

= \frac{33}{4}

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