What is the integral from 0 to infinity of ze^{-z^2} ?

The integral from 0 to infinity of ze^{-z^2} is 1/2

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integral from 0 to infinity of ze^{-z^2}

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

= \frac{1}{2}

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