What is the integral from 2 to 4 of xe^{-x/2} ?

The integral from 2 to 4 of xe^{-x/2} is -(12)/(e^2)+8/e

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integral from 2 to 4 of xe^{-x/2}

\int_{2}^{4} x e^{- \frac{x}{2}} d x

- \frac{12}{e ^{2}} + \frac{8}{e}

Decimal

1.31901 \dots

Solution steps

\int_{2}^{4} 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]_{2}^{4}

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

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

Compute the boundaries:

- \frac{12}{e ^{2}} + \frac{8}{e}

= - \frac{12}{e ^{2}} + \frac{8}{e}

What is the integral from 2 to 4 of xe^{-x/2} ?
The integral from 2 to 4 of xe^{-x/2} is -(12)/(e^2)+8/e