Integrating the Gaussian Integral: Is it as Easy as It Seems?

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Discussion Overview

The discussion revolves around the Gaussian integral, specifically its evaluation from negative to positive infinity and related concepts such as the Error Function. Participants explore the challenges and nuances involved in integrating this function, including potential misunderstandings related to coordinate systems.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants mention the Gaussian integral is defined from negative to positive infinity and suggest the Error Function as a related concept for integration.
  • One participant reflects on a misunderstanding regarding the bounds of the Error Function, indicating a common source of confusion.
  • A participant shares a personal anecdote about a housemate's difficulties with the integral, noting that the issue was resolved by transforming the coordinates.
  • Another participant humorously suggests that integrating the Gaussian integral with respect to x is straightforward.
  • There is a reference to a related discussion in another thread, indicating ongoing conversations about the topic.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints and some confusion regarding the integration of the Gaussian integral and the Error Function. No consensus is reached on the ease of integration or the best approach to take.

Contextual Notes

Participants express uncertainty about the bounds of the Error Function and the implications of coordinate transformations on the integration process. There are unresolved details about the integration steps and the context of the problem being discussed.

Zurtex
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From memory the Gaussian integral is from infinity to negative infinity..if you want something that act's as an anti derivative, try the Error Function ( erf(x) )

EDIT: ~sigh~ I just realized the erf(x) also has bounds, my bad.
 
Gib Z said:
From memory the Gaussian integral is from infinity to negative infinity..if you want something that act's as an anti derivative, try the Error Function ( erf(x) )

EDIT: ~sigh~ I just realized the erf(x) also has bounds, my bad.

Thanks, the problem was actually in response to a house mate on a physics course who had this integral and was utterly perplexed how one would integrate it from negative to positive infinity. I remembered it was a standard integral but forgot the details how to do it, anyway in the end it turned out he was integrating over the wrong co-ordinates anyway and it was much more simple once he transformed the integral.

But thanks for trying :smile:
 
how about integrating it wrt x. Easy!
 

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