Multivariate Function Integration

[gordonj005]

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

 

[mathman]

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.

 

[gordonj005]

What do you mean by "nice" integrands?

Ah right, that's what I thought. Thanks a lot man.

 

[Charles49]

Look up Fubini theorem.

 

[Char. Limit]

For the second question, this might help you understand:

http://www.cliffsnotes.com/study_guide/Partial-Integration.topicArticleId-19736,articleId-19707.html [Broken]