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Popular Calculus >

integral from-1 to 1 of (|x|-1)

Solution

\int_{- 1}^{1} (∣ x ∣ - 1) d x

Solution

- 1

Solution steps

\int_{- 1}^{1} ∣ x ∣ - 1 d x

Eliminate Absolutes

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

\int_{- 1}^{0} - x - 1 d x = - \frac{1}{2}

\int_{0}^{1} x - 1 d x = - \frac{1}{2}

= - \frac{1}{2} - \frac{1}{2}

Simplify

- \frac{1}{2} - \frac{1}{2} : - 1

= - 1

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-1 to 1 of (|x|-1) ?
The integral from-1 to 1 of (|x|-1) is -1