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

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

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

\int_{- \infty}^{- 1} x e^{- x^{2}} d x

- \frac{1}{2 e}

Decimal Notation

- 0.18393 \dots

Solution steps

\int_{- \infty}^{- 1} x e^{- x^{2}} d x

Compute the indefinite integral:

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

Compute the boundaries:

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

= - \frac{1}{2 e} - 0

Simplify

= - \frac{1}{2 e}

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