What is the integral from 0 to-1 of xe^{-x} ?

The integral from 0 to-1 of xe^{-x} is 1

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integral from 0 to-1 of xe^{-x}

\int_{0}^{- 1} x e^{- x} d x

1

Solution steps

\int_{0}^{- 1} x e^{- x} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 1}^{0} x e^{- x} d x

Apply Integration By Parts

: [- e^{- x} x - \int - e^{- x} d x]_{- 1}^{0}

= - [- e^{- x} x - \int - e^{- x} d x]_{- 1}^{0}

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

= - [- e^{- x} x - e^{- x}]_{- 1}^{0}

Compute the boundaries:

- 1

= - (- 1)

Simplify

= 1

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