What is the integral from 0 to infinity of ce^{-ax} ?

The integral from 0 to infinity of ce^{-ax} is c/a

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integral from 0 to infinity of ce^{-ax}

\int_{0}^{\infty} c e^{- a x} d x

\frac{c}{a}

Solution steps

\int_{0}^{\infty} c e^{- a x} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} c e^{- a x} d x = 0 - (- \frac{c}{a})

= 0 - (- \frac{c}{a})

Simplify

= \frac{c}{a}

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What is the integral from 0 to infinity of ce^{-ax} ?
The integral from 0 to infinity of ce^{-ax} is c/a