Can the integral of e^(x^2) be solved for arbitrary limits?

  • Context: Graduate 
  • Thread starter Thread starter ep10
  • Start date Start date
  • Tags Tags
    Integral
Click For Summary

Discussion Overview

The discussion revolves around the integral of the function e^(-x^2) with arbitrary limits from a to infinity. Participants explore the challenges of solving this integral, particularly in relation to its connection with the error function and the nature of non-elementary functions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses difficulty in solving the integral of e^(-x^2) from arbitrary limits a to infinity, noting ease with the 0 to infinity case.
  • Another participant suggests that the integral relates to a Gaussian function and mentions the error function as the anti-derivative, indicating its non-elementary nature.
  • A third participant acknowledges the previous points but expresses uncertainty about how to proceed with the solution.
  • A later reply asserts that the integral cannot be solved in terms of elementary functions, reiterating the non-elementary status of the error function.

Areas of Agreement / Disagreement

Participants generally agree that the integral cannot be expressed in terms of elementary functions and that it involves the error function, but there remains uncertainty about how to approach the problem with arbitrary limits.

Contextual Notes

The discussion highlights the limitations of using elementary functions for this integral and the dependence on the properties of the error function, but does not resolve the specific steps needed to evaluate the integral from a to infinity.

ep10
Messages
3
Reaction score
0
i am solving a problem that involves taking the integral of an exponential to the power of -x^2. I would have no problem solving this integral if the limits were 0 to infinity but the limits i am solving for are an arbitrary a to infinity. Can anybody help?
 
Physics news on Phys.org
ep10 said:
i am solving a problem that involves taking the integral of an exponential to the power of -x^2. I would have no problem solving this integral if the limits were 0 to infinity but the limits i am solving for are an arbitrary a to infinity. Can anybody help?

Sounds like a gaussian function:
http://en.wikipedia.org/wiki/Normal_distribution

The anti-derivative is the error function, which is nonelementary.
 
that verifies what i was thinking but i am still having trouble going about solving it. I think I am just not sure where to start. Thanks though at least I know I am not completely off track
 
You can't solve it, in terms of elementary functions, that is. As Tac-Tics already said, the error function is non-elementary.
 

Similar threads

Graduate Multiplying divergent integrals using Hardy fields approach
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad What's my mistake in this integration problem?
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Memory issues in numerical integration of oscillatory function
  • · Replies 3 ·
Replies
3
Views
2K
High School Straightforward integration…
  • · Replies 27 ·
Replies
27
Views
3K
High School Is it possible to find the integral of ##f(x)/x^2##?
  • · Replies 8 ·
Replies
8
Views
2K
High School Question about the limits of integration in a change of variables
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Result of this integral in large Lambda limit
  • · Replies 12 ·
Replies
12
Views
3K
Graduate Need help with an integral -- How to integrate velocity squared?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Determining Whether Solution is Vector vs Scalar?
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad ##L^2## square integrable function Hilbert space
  • · Replies 11 ·
Replies
11
Views
3K