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

The integral from 0 to infinity of e^{-px} is 1/p

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

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

\frac{1}{p}

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

= \frac{1}{p}

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