What is the integral from 0 to infinity of ke^{-x} ?

The integral from 0 to infinity of ke^{-x} is k

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integral from 0 to infinity of ke^{-x}

\int_{0}^{\infty} k e^{- x} d x

k

Solution steps

\int_{0}^{\infty} k e^{- x} d x

Compute the indefinite integral:

\int k e^{- x} d x = - k e^{- x} + C

Compute the boundaries:

\int_{0}^{\infty} k e^{- x} d x = 0 - (- k)

= 0 - (- k)

Simplify

= k

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What is the integral from 0 to infinity of ke^{-x} ?
The integral from 0 to infinity of ke^{-x} is k