WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Some Gaussian Integrals

​
n
0
1
2
3
b
1
2
3
4
5
p
1
p
∫
0
n
x
-b
2
x
e
dx = 0.31606
The well-known Gaussian integral
∞
∫
0
-
2
x
e
dx=
π
2
can be evaluated in closed form, even though there is no elementary function equal to the indefinite integral
∫
-
2
x
e
dx
. More generally, integrals of the form
∞
∫
0
n
x
-b
2
x
e
dx
can be evaluated for positive integers
n
[1]. In this Demonstration, we perform numerical integrations for
p
∫
0
n
x
-b
2
x
e
dx
, with
n=0,1,2,3
and
b=1,2,…,5
. The results are then represented as areas under a curve (shown in red).
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.