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

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

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integral from 1 to 2 of xe^{-x}

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

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

Decimal

0.32975 \dots

Solution steps

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

Apply Integration By Parts

= [- 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}

\int_{8}^{17} x x^{2} - 64 d x

\int_{0}^{3} \frac{x e ^{x}}{( 1 + x ) ^{2}} d x

\int_{y}^{\infty} e^{- x} d x

\int_{0}^{x} y d y

\int_{0}^{1} (3 + x^{2})^{2} x d x

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