What is the integral from 0 to infinity of e^{-|x|} ?

The integral from 0 to infinity of e^{-|x|} is 1

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integral from 0 to infinity of e^{-|x|}

\int_{0}^{\infty} e^{- ∣ x ∣} d x

1

Solution steps

\int_{0}^{\infty} e^{- ∣ x ∣} d x

Eliminate Absolutes

= \int_{0}^{\infty} e^{- x} d x

Compute the indefinite integral:

\int e^{- x} d x = - e^{- x} + C

Compute the boundaries:

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

= 0 - (- 1)

Simplify

= 1

What is the integral from 0 to infinity of e^{-|x|} ?
The integral from 0 to infinity of e^{-|x|} is 1