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

The integral from 1 to 2 of x*e^{-x} is -3/(e^2)+2/e

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integral from 1 to 2 of x*e^{-x}

\int_{1}^{2} x \cdot e^{- x} d x

- \frac{3}{e ^{2}} + \frac{2}{e}

Solution steps

\int_{1}^{2} x e^{- x} d x

Apply Integration By Parts

: [- e^{- x} x - \int - e^{- x} d x]_{1}^{2}

= [- e^{- x} x - \int - e^{- x} d x]_{1}^{2}

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

= [- e^{- x} x - e^{- x}]_{1}^{2}

Compute the boundaries:

- \frac{3}{e ^{2}} + \frac{2}{e}

= - \frac{3}{e ^{2}} + \frac{2}{e}

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What is the integral from 1 to 2 of x*e^{-x} ?
The integral from 1 to 2 of x*e^{-x} is -3/(e^2)+2/e