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

The integral from 0 to infinity of xe^{-y} is x

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

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

x

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- x)

Simplify

= x

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