integral from-4 to 3 of 12-x-x^2

解答

\int_{- 4}^{3} 12 - x - x^{2} d x

\frac{343}{6}

十进制

57.16666 \dots

求解步骤

\int_{- 4}^{3} 12 - x - 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_{- 4}^{3} 12 d x - \int_{- 4}^{3} x d x - \int_{- 4}^{3} x^{2} d x

\int_{- 4}^{3} 12 d x = 84

\int_{- 4}^{3} x d x = - \frac{7}{2}

\int_{- 4}^{3} x^{2} d x = \frac{91}{3}

= 84 - (- \frac{7}{2}) - \frac{91}{3}

化简

84 - (- \frac{7}{2}) - \frac{91}{3} : \frac{343}{6}

= \frac{343}{6}

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