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

The integral from-infinity to 0 of xe^{x/2} is -4

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

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

- 4

Solution steps

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

Compute the indefinite integral:

\int x e^{\frac{x}{2}} d x = 4 (\frac{1}{2} e^{\frac{x}{2}} x - e^{\frac{x}{2}}) + C

Compute the boundaries:

\int_{- \infty}^{0} x e^{\frac{x}{2}} d x = - 4 - 0

= - 4 - 0

Simplify

= - 4

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What is the integral from-infinity to 0 of xe^{x/2} ?
The integral from-infinity to 0 of xe^{x/2} is -4