What is the integral from 0 to infinity of e^{-2at} ?

The integral from 0 to infinity of e^{-2at} is 1/(2a)

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integral from 0 to infinity of e^{-2at}

\int_{0}^{\infty} e^{- 2 a t} d t

\frac{1}{2 a}

Solution steps

\int_{0}^{\infty} e^{- 2 a t} d t

Compute the indefinite integral:

\int e^{- 2 a t} d t = - \frac{1}{2 a} e^{- 2 a t} + C

Compute the boundaries:

\int_{0}^{\infty} e^{- 2 a t} d t = 0 - (- \frac{1}{2 a})

= 0 - (- \frac{1}{2 a})

Simplify

= \frac{1}{2 a}

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What is the integral from 0 to infinity of e^{-2at} ?
The integral from 0 to infinity of e^{-2at} is 1/(2a)