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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

= \frac{1}{2} - 0

Simplify

= \frac{1}{2}

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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 1/2