What is the integral from-1 to 1 of e^{-|x|} ?

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

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integral from-1 to 1 of e^{-|x|}

\int_{- 1}^{1} e^{- ∣ x ∣} d x

- \frac{2}{e} + 2

Decimal Notation

1.26424 \dots

Solution steps

\int_{- 1}^{1} e^{- ∣ x ∣} d x

Eliminate Absolutes

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

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

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

= 1 - \frac{1}{e} + 1 - \frac{1}{e}

Simplify

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

= - \frac{2}{e} + 2

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

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

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