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

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

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

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

\frac{1}{2 e}

Decimal Notation

0.18393 \dots

Solution steps

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

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

Simplify

= \frac{1}{2 e}

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