What is the integral from 0 to N of xe^{-x} ?

The integral from 0 to N of xe^{-x} is -Ne^{-N}-e^{-N}+1

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integral from 0 to N of xe^{-x}

\int_{0}^{N} x e^{- x} d x

- N e^{- N} - e^{- N} + 1

Solution steps

\int_{0}^{N} x e^{- x} d x

Apply Integration By Parts

= [- e^{- x} x - \int - e^{- x} d x]_{0}^{N}

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

= [- e^{- x} x - e^{- x}]_{0}^{N}

Compute the boundaries:

- N e^{- N} - e^{- N} + 1

= - N e^{- N} - e^{- N} + 1

What is the integral from 0 to N of xe^{-x} ?
The integral from 0 to N of xe^{-x} is -Ne^{-N}-e^{-N}+1