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#1 2007-10-27 10:50:15

Sekky
Member
Registered: 2007-01-12
Posts: 181

Reversing the Order of Integration

I've asked several people to explain this to me and each time they draw me some stupid little picture of a specific example and call it a proof and expect me to generalise it, so can somebody please explain to me algebraically how to generalise reversing the order of integrals.

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#2 2007-10-27 13:45:09

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: Reversing the Order of Integration

It doesn't matter whether you finish a map puzzle row by row or column by column (Imagine you can do that).


X'(y-Xβ)=0

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#3 2007-10-27 19:59:31

Sekky
Member
Registered: 2007-01-12
Posts: 181

Re: Reversing the Order of Integration

That in no way answered my question

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#4 2007-10-27 20:06:39

Sekky
Member
Registered: 2007-01-12
Posts: 181

Re: Reversing the Order of Integration

Maybe my question isn't clear.

How do you reverse this integral?

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#5 2007-10-29 05:16:42

George,Y
Member
Registered: 2006-03-12
Posts: 1,379

Re: Reversing the Order of Integration

I have no idea. My explaination is only to the constant integration region (The fixed rectangle).


X'(y-Xβ)=0

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#6 2007-10-29 09:09:51

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Reversing the Order of Integration

The theorem is known as Change of Variables.  Here is a link to a proof:

www.math.ucsd.edu/programs/undergraduat … change.pdf


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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