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

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

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

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

\frac{π}{2}

Decimal

1.25331 \dots

Solution steps

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

Compute the indefinite integral:

\int e^{\frac{- x ^{2}}{2}} d x = (\frac{π}{2})^{\frac{1}{2}} erf (\frac{x}{2}) + C

Compute the boundaries:

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

= \frac{π}{2} - 0

Simplify

= \frac{π}{2}

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