What is the integral from 0 to infinity of Ae^{-λt} ?

The integral from 0 to infinity of Ae^{-λt} is A/λ

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integral from 0 to infinity of Ae^{-λt}

\int_{0}^{\infty} A e^{- λ t} d t

\frac{A}{λ}

Solution steps

\int_{0}^{\infty} A e^{- λ t} d t

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} A e^{- λ t} d t = 0 - (- \frac{A}{λ})

= 0 - (- \frac{A}{λ})

Simplify

= \frac{A}{λ}

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What is the integral from 0 to infinity of Ae^{-λt} ?
The integral from 0 to infinity of Ae^{-λt} is A/λ