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

The integral from-1 to 1 of xe^{-x} is -2/e

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

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

- \frac{2}{e}

Decimal

- 0.73575 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

Compute the boundaries:

- \frac{2}{e}

= - \frac{2}{e}

What is the integral from-1 to 1 of xe^{-x} ?
The integral from-1 to 1 of xe^{-x} is -2/e