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

The integral from 0 to infinity of e^{-kx} is 1/k

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integral from 0 to infinity of e^{-kx}

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

\frac{1}{k}

Solution steps

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

Compute the indefinite integral:

\int e^{- k x} d x = - \frac{1}{k} e^{- k x} + C

Compute the boundaries:

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

= 0 - (- \frac{1}{k})

Simplify

= \frac{1}{k}

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What is the integral from 0 to infinity of e^{-kx} ?
The integral from 0 to infinity of e^{-kx} is 1/k