What is the integral from-2 to 2 of (|x|-x)e^{-|x|} ?

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

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integral from-2 to 2 of (|x|-x)e^{-|x|}

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

- 2 (\frac{3}{e ^{2}} - 1)

Decimal

1.18798 \dots

Solution steps

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

Eliminate Absolutes

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

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

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

= - 2 (- 1 + \frac{3}{e ^{2}}) + 0

Simplify

= - 2 (\frac{3}{e ^{2}} - 1)

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