What is the integral from 0 to infinity of 5e^{-5t} ?

The integral from 0 to infinity of 5e^{-5t} is 1

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integral from 0 to infinity of 5e^{-5t}

\int_{0}^{\infty} 5 e^{- 5 t} d t

1

Solution steps

\int_{0}^{\infty} 5 e^{- 5 t} d t

Compute the indefinite integral:

\int 5 e^{- 5 t} d t = - e^{- 5 t} + C

Compute the boundaries:

\int_{0}^{\infty} 5 e^{- 5 t} d t = 0 - (- 1)

= 0 - (- 1)

Simplify

= 1

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What is the integral from 0 to infinity of 5e^{-5t} ?
The integral from 0 to infinity of 5e^{-5t} is 1