What is the integral from 0 to 1 of xe^{-x/2} ?

The integral from 0 to 1 of xe^{-x/2} is -6/(e^{1/2)}+4

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integral from 0 to 1 of xe^{-x/2}

\int_{0}^{1} x e^{- \frac{x}{2}} d x

- \frac{6}{e ^{\frac{1}{2}}} + 4

Decimal

0.36081 \dots

Solution steps

\int_{0}^{1} x e^{- \frac{x}{2}} d x

Apply Integration By Parts

: [- 2 e^{- \frac{x}{2}} x - \int - 2 e^{- \frac{x}{2}} d x]_{0}^{1}

= [- 2 e^{- \frac{x}{2}} x - \int - 2 e^{- \frac{x}{2}} d x]_{0}^{1}

\int - 2 e^{- \frac{x}{2}} d x = 4 e^{- \frac{x}{2}}

= [- 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}}]_{0}^{1}

Compute the boundaries:

- \frac{6}{e ^{\frac{1}{2}}} + 4

= - \frac{6}{e ^{\frac{1}{2}}} + 4

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What is the integral from 0 to 1 of xe^{-x/2} ?
The integral from 0 to 1 of xe^{-x/2} is -6/(e^{1/2)}+4