What is the integral from 1 to 4 of xe^{-x} ?

The integral from 1 to 4 of xe^{-x} is -5/(e^4)+2/e

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integral from 1 to 4 of xe^{-x}

\int_{1}^{4} x e^{- x} d x

- \frac{5}{e ^{4}} + \frac{2}{e}

Decimal

0.64418 \dots

Solution steps

\int_{1}^{4} x e^{- x} d x

Apply Integration By Parts

: [- e^{- x} x - \int - e^{- x} d x]_{1}^{4}

= [- e^{- x} x - \int - e^{- x} d x]_{1}^{4}

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

= [- e^{- x} x - e^{- x}]_{1}^{4}

Compute the boundaries:

- \frac{5}{e ^{4}} + \frac{2}{e}

= - \frac{5}{e ^{4}} + \frac{2}{e}

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What is the integral from 1 to 4 of xe^{-x} ?
The integral from 1 to 4 of xe^{-x} is -5/(e^4)+2/e