Multivariate Function Integration

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The order of integration in multiple integrals of a multivariable function does not matter for "nice" integrands, according to Fubini's theorem. When partially integrating a multivariable function, one can integrate with respect to a specific variable while keeping others constant, indicated by the differentials used. The notation for this involves specifying the variable of integration, such as f(x,y)dx, which means integrating with respect to x while treating y as a constant. Understanding these concepts can clarify the integration process in multivariable calculus. The discussion emphasizes the importance of recognizing the properties of the integrands involved.
gordonj005
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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
 
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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.
 
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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
 
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