Some Gaussian Integrals
Some Gaussian Integrals
The wellknown Gaussian integral dx= can be evaluated in closed form, even though there is no elementary function equal to the indefinite integral . More generally, integrals of the form dx can be evaluated for positive integers [1]. In this Demonstration, we perform numerical integrations for dx, with and . The results are then represented as areas under a curve (shown in red).
∞
∫
0

2
x
e
π
2
∫dx

2
x
e
∞
∫
0
n
x
b
2
x
e
n
p
∫
0
n
x
b
2
x
e
n=0,1,2,3
b=1,2,…,5