integral from-2 to 4 of |x-1|

解答

\int_{- 2}^{4} ∣ x - 1 ∣ d x

9

求解步骤

\int_{- 2}^{4} ∣ x - 1 ∣ d x

拿掉绝对值

= \int_{- 2}^{1} - x + 1 d x + \int_{1}^{4} x - 1 d x

\int_{- 2}^{1} - x + 1 d x = \frac{9}{2}

\int_{1}^{4} x - 1 d x = \frac{9}{2}

= \frac{9}{2} + \frac{9}{2}

化简

\frac{9}{2} + \frac{9}{2} : 9

= 9

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