What is the integral from 0 to infinity of e^{-u^2} ?

The integral from 0 to infinity of e^{-u^2} is (sqrt(pi))/2

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integral from 0 to infinity of e^{-u^2}

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

\frac{π}{2}

Decimal Notation

0.88622 \dots

Solution steps

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

Compute the indefinite integral:

\int e^{- u^{2}} d u = \frac{π}{2} erf (u) + C

Compute the boundaries:

\int_{0}^{\infty} e^{- u^{2}} d u = \frac{π}{2} - 0

= \frac{π}{2} - 0

Simplify

= \frac{π}{2}

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What is the integral from 0 to infinity of e^{-u^2} ?
The integral from 0 to infinity of e^{-u^2} is (sqrt(pi))/2