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

The integral from 0 to infinity of e^{-at} is 1/a

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

\int_{0}^{\infty} e^{- a t} d t

\frac{1}{a}

Solution steps

\int_{0}^{\infty} e^{- a t} d t

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} e^{- a t} d t = 0 - (- \frac{1}{a})

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

Simplify

= \frac{1}{a}

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