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

The integral from 1 to 0 of xe^{-x} is 2/e-1

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

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

\frac{2}{e} - 1

Decimal

- 0.26424 \dots

Solution steps

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

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

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

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

- \frac{2}{e} + 1

= - (- \frac{2}{e} + 1)

Simplify

= \frac{2}{e} - 1

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What is the integral from 1 to 0 of xe^{-x} ?
The integral from 1 to 0 of xe^{-x} is 2/e-1