# Some Gaussian Integrals

Some Gaussian Integrals

The well-known Gaussian integral can be evaluated in closed form, even though there is no elementary function equal to the indefinite integral . More generally, integrals of the form can be evaluated for positive integers [1]. In this Demonstration, we perform numerical integrations for , with and . The results are then represented as areas under a curve (shown in red).

∫edx=

∞

0

-x

2

π

2

∫edx

-x

2

∫xedx

∞

0

n

-bx

2

n

∫xedx

p

0

n

-bx

2

n=0,1,2,3

b=1,2,…,5