What is the integral from-infinity to 0 of e^{-|6x|} ?

The integral from-infinity to 0 of e^{-|6x|} is 1/6

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integral from-infinity to 0 of e^{-|6x|}

\int_{- \infty}^{0} e^{- ∣ 6 x ∣} d x

\frac{1}{6}

Decimal Notation

0.16666 \dots

Solution steps

\int_{- \infty}^{0} e^{- ∣ 6 x ∣} d x

Eliminate Absolutes

= \int_{- \infty}^{0} e^{- (- 6 x)} d x

Compute the indefinite integral:

\int e^{- (- 6 x)} d x = \frac{1}{6} e^{6 x} + C

Compute the boundaries:

\int_{- \infty}^{0} e^{- (- 6 x)} d x = \frac{1}{6} - 0

= \frac{1}{6} - 0

Simplify

= \frac{1}{6}

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What is the integral from-infinity to 0 of e^{-|6x|} ?
The integral from-infinity to 0 of e^{-|6x|} is 1/6