What is the integral from-1 to 0 of |x| ?

The integral from-1 to 0 of |x| is 1/2

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integral from-1 to 0 of |x|

\int_{- 1}^{0} ∣ x ∣ d x

\frac{1}{2}

Decimal Notation

0.5

Solution steps

\int_{- 1}^{0} ∣ x ∣ d x

Eliminate Absolutes

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{- 1}^{0}

= - [\frac{x ^{2}}{2}]_{- 1}^{0}

Compute the boundaries:

- \frac{1}{2}

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

Simplify

= \frac{1}{2}

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What is the integral from-1 to 0 of |x| ?
The integral from-1 to 0 of |x| is 1/2