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

The integral from 0 to infinity of e^{-r^2}r is 1/2

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^{-r^2}r

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

\frac{1}{2}

Decimal

0.5

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

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

Simplify

= \frac{1}{2}

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