integral from-2 to 5 of (x^2-4x-3)

解答

\int_{- 2}^{5} (x^{2} - 4 x - 3) d x

- \frac{56}{3}

十进制

- 18.66666 \dots

求解步骤

\int_{- 2}^{5} x^{2} - 4 x - 3 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_{- 2}^{5} x^{2} d x - \int_{- 2}^{5} 4 x d x - \int_{- 2}^{5} 3 d x

\int_{- 2}^{5} x^{2} d x = \frac{133}{3}

\int_{- 2}^{5} 4 x d x = 42

\int_{- 2}^{5} 3 d x = 21

= \frac{133}{3} - 42 - 21

化简

\frac{133}{3} - 42 - 21 : - \frac{56}{3}

= - \frac{56}{3}

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