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

The integral from y to infinity of xe^{-x} is -(-e^{-y}y-e^{-y})

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

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

- (- e^{- y} y - e^{- y})

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= 0 - (- e^{- y} y - e^{- y})

Simplify

= - (- e^{- y} y - e^{- y})

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