Multivariate Function Integration

Click For Summary

Discussion Overview

The discussion revolves around the integration of multivariable functions, specifically addressing whether the order of integration matters and the notation for partially integrating with respect to a single variable. The scope includes theoretical aspects of integration and notation conventions.

Discussion Character

  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that the order of integration does not matter for "nice" integrands, though the definition of "nice" is questioned.
  • One participant indicates that partial integration can be denoted by the differentials used, suggesting that integrating with respect to one variable while leaving others alone is standard practice.
  • A participant references Fubini's theorem as relevant to the discussion of integration order.
  • Another participant provides a link to an external resource that may clarify the concept of partial integration.

Areas of Agreement / Disagreement

There is no consensus on what constitutes "nice" integrands, and the discussion includes varying interpretations of the notation for partial integration. Multiple viewpoints remain without resolution.

Contextual Notes

The discussion does not clarify the specific conditions under which the order of integration may or may not matter, nor does it resolve the implications of the Fubini theorem in this context.

gordonj005
Messages
56
Reaction score
0
Quick Question

When taking multiple integrals of a multivariable function, does the order in which you integrate (in terms of the variable) matter?

Also, is there a notation for partially integrating a multivariable function with respect to a single variable?

Thanks for your help
 
Physics news on Phys.org
The order will not matter for "nice" integrands.

I'm not sure what you are looking for in your second question. You can integrate with respect to some variables and leave others alone. This would be indicated by what differentials you use. For example the integral of f(x,y)dx means integrate with respect to x and leave y alone.
 
Last edited:
What do you mean by "nice" integrands?

Ah right, that's what I thought. Thanks a lot man.
 
Look up Fubini theorem.
 
For the second question, this might help you understand:

http://www.cliffsnotes.com/study_guide/Partial-Integration.topicArticleId-19736,articleId-19707.html
 
Last edited by a moderator:

Similar threads

  • · Replies 21 ·
Replies
21
Views
6K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 10 ·
Replies
10
Views
3K
Replies
2
Views
982
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 31 ·
2
Replies
31
Views
5K