What is the integral from 0 to 4 of xe^{-x/4} ?

The integral from 0 to 4 of xe^{-x/4} is -(32)/e+16

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integral from 0 to 4 of xe^{-x/4}

\int_{0}^{4} x e^{- \frac{x}{4}} d x

- \frac{32}{e} + 16

Decimal Notation

4.22785 \dots

Solution steps

\int_{0}^{4} x e^{- \frac{x}{4}} d x

Apply Integration By Parts

: [- 4 e^{- \frac{x}{4}} x - \int - 4 e^{- \frac{x}{4}} d x]_{0}^{4}

= [- 4 e^{- \frac{x}{4}} x - \int - 4 e^{- \frac{x}{4}} d x]_{0}^{4}

\int - 4 e^{- \frac{x}{4}} d x = 16 e^{- \frac{x}{4}}

= [- 4 e^{- \frac{x}{4}} x - 16 e^{- \frac{x}{4}}]_{0}^{4}

Compute the boundaries:

- \frac{32}{e} + 16

= - \frac{32}{e} + 16

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What is the integral from 0 to 4 of xe^{-x/4} ?
The integral from 0 to 4 of xe^{-x/4} is -(32)/e+16