What is the integral from-infinity to 0 of e^{-|3x|} ?

The integral from-infinity to 0 of e^{-|3x|} is 1/3

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integral from-infinity to 0 of e^{-|3x|}

\int_{- \infty}^{0} e^{- ∣ 3 x ∣} d x

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

\int_{- \infty}^{0} e^{- ∣ 3 x ∣} d x

Eliminate Absolutes

= \int_{- \infty}^{0} e^{- (- 3 x)} d x

Compute the indefinite integral:

\int e^{- (- 3 x)} d x = \frac{1}{3} e^{3 x} + C

Compute the boundaries:

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

= \frac{1}{3} - 0

Simplify

= \frac{1}{3}

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What is the integral from-infinity to 0 of e^{-|3x|} ?
The integral from-infinity to 0 of e^{-|3x|} is 1/3