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

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

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integral from-2 to 2 of 1/2 (1-(|x|)/2)

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

1

Solution steps

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

Eliminate Absolutes

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

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

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

= \frac{1}{2} + \frac{1}{2}

Simplify

\frac{1}{2} + \frac{1}{2} : 1

= 1

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