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

解答

\int_{- 2}^{2} ∣ x ∣ - ∣ x - 1 ∣ d x

- 1

求解步骤

\int_{- 2}^{2} ∣ x ∣ - ∣ x - 1 ∣ d x

拿掉绝对值

= \int_{- 2}^{0} - x - (- x + 1) d x + \int_{0}^{1} x - (- x + 1) d x + \int_{1}^{2} x - (x - 1) d x

\int_{- 2}^{0} - x - (- x + 1) d x = - 2

\int_{0}^{1} x - (- x + 1) d x = 0

\int_{1}^{2} x - (x - 1) d x = 1

= - 2 + 0 + 1

化简

= - 1

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