What is the integral from 0 to infinity of ye^{-y} ?

The integral from 0 to infinity of ye^{-y} is 1

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integral from 0 to infinity of ye^{-y}

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

1

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- 1)

Simplify

= 1

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