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

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

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

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

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

Simplify

= \frac{1}{2}

\frac{\partial}{\partial y} (\frac{1}{x - y})

2

f (x) = \frac{9}{x ^{2} + 5}

cos^{2} (x), 0

sin (x) + \frac{4}{9} cot (x)

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