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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{π}{2}

Decimal

0.88622 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{π}{2} - 0

Simplify

= \frac{π}{2}

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