integral from-4 to 4 of |x^2+x-6|

解答

\int_{- 4}^{4} x^{2} + x - 6 d x

\frac{109}{3}

十进制

36.33333 \dots

求解步骤

\int_{- 4}^{4} x^{2} + x - 6 d x

拿掉绝对值

= \int_{- 4}^{- 3} x^{2} + x - 6 d x + \int_{- 3}^{2} - x^{2} - x + 6 d x + \int_{2}^{4} x^{2} + x - 6 d x

\int_{- 4}^{- 3} x^{2} + x - 6 d x = \frac{17}{6}

\int_{- 3}^{2} - x^{2} - x + 6 d x = \frac{125}{6}

\int_{2}^{4} x^{2} + x - 6 d x = \frac{38}{3}

= \frac{17}{6} + \frac{125}{6} + \frac{38}{3}

化简

\frac{17}{6} + \frac{125}{6} + \frac{38}{3} : \frac{109}{3}

= \frac{109}{3}

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