What is the integral from-1 to 2 of (|x|-1)^3 ?

The integral from-1 to 2 of (|x|-1)^3 is -1/4

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integral from-1 to 2 of (|x|-1)^3

\int_{- 1}^{2} (∣ x ∣ - 1)^{3} d x

- \frac{1}{4}

Solution steps

\int_{- 1}^{2} (∣ x ∣ - 1)^{3} d x

Eliminate Absolutes

= \int_{- 1}^{0} (- x - 1)^{3} d x + \int_{0}^{2} (x - 1)^{3} d x

\int_{- 1}^{0} (- x - 1)^{3} d x = - \frac{1}{4}

\int_{0}^{2} (x - 1)^{3} d x = 0

= - \frac{1}{4} + 0

Simplify

= - \frac{1}{4}

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What is the integral from-1 to 2 of (|x|-1)^3 ?
The integral from-1 to 2 of (|x|-1)^3 is -1/4