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

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SUMMARY

The Gaussian integral, defined from negative to positive infinity, is a standard integral often encountered in physics and mathematics. The Error Function (erf(x)) serves as an anti-derivative for the Gaussian integral, although it also has specific bounds. A common issue arises when integrating over incorrect coordinates, which can complicate the process. Transforming the integral to the correct coordinates simplifies the integration significantly.

PREREQUISITES
  • Understanding of the Gaussian integral
  • Familiarity with the Error Function (erf(x))
  • Basic knowledge of integral calculus
  • Concept of coordinate transformation in integration
NEXT STEPS
  • Study the properties and applications of the Gaussian integral
  • Learn about the Error Function (erf) and its significance in probability and statistics
  • Explore coordinate transformations in integral calculus
  • Investigate common pitfalls in integrating functions over infinite bounds
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Students and professionals in mathematics, physics, and engineering who are dealing with integrals, particularly those involving Gaussian functions and error analysis.

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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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