What is the integral from 2 to 3 of xe^{-x} ?

The integral from 2 to 3 of xe^{-x} is -4/(e^3)+3/(e^2)

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integral from 2 to 3 of xe^{-x}

\int_{2}^{3} x e^{- x} d x

- \frac{4}{e ^{3}} + \frac{3}{e ^{2}}

Decimal Notation

0.20685 \dots

Solution steps

\int_{2}^{3} x e^{- x} d x

Apply Integration By Parts

: [- e^{- x} x - \int - e^{- x} d x]_{2}^{3}

= [- e^{- x} x - \int - e^{- x} d x]_{2}^{3}

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

= [- e^{- x} x - e^{- x}]_{2}^{3}

Compute the boundaries:

- \frac{4}{e ^{3}} + \frac{3}{e ^{2}}

= - \frac{4}{e ^{3}} + \frac{3}{e ^{2}}

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What is the integral from 2 to 3 of xe^{-x} ?
The integral from 2 to 3 of xe^{-x} is -4/(e^3)+3/(e^2)