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

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

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

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

\frac{π}{2}

Decimal Notation

0.88622 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{π}{2} - 0

Simplify

= \frac{π}{2}

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\frac{d}{d t} (\frac{6}{5} - t^{2})

\frac{x ^{2}}{8}, 2 x^{2}, 2, 0

n = 1 \sum \infty n! x^{n}

\frac{d}{d y} (x y 1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{9})

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