What is the integral from 0 to infinity of re^{-r} ?

The integral from 0 to infinity of re^{-r} is 1

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integral from 0 to infinity of re^{-r}

\int_{0}^{\infty} r e^{- r} d r

1

Solution steps

\int_{0}^{\infty} r e^{- r} d r

Compute the indefinite integral:

\int r e^{- r} d r = - e^{- r} r - e^{- r} + C

Compute the boundaries:

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

= 0 - (- 1)

Simplify

= 1

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What is the integral from 0 to infinity of re^{-r} ?
The integral from 0 to infinity of re^{-r} is 1