order of integration..the core

**corleone2463** · August 25th 2009, 04:00 AM

hello everybody
i want to know that if we have a multivariable function f(x,y)
then

$\int \int f(x,y) ~dydx = \int \int f(x,y) ~dxdy$

wen is this true ...are there any conditions for it or is it always true...

**Prove It** · August 25th 2009, 04:03 AM

Originally Posted by corleone2463

hello everybody
i want to know that if we have a multivariable function f(x,y)
then

$\int \int f(x,y) ~dydx = \int \int f(x,y) ~dxdy$

wen is this true ...are there any conditions for it or is it always true...

It is always true as long as you get the terminals of your integral right.

**nirax** · August 25th 2009, 04:18 AM

see Fubini's theorem in wikipedia.

**corleone2463** · August 25th 2009, 04:27 AM

you people are all talking about the definite integrals where we integrate a function over a defined 2-d region in this case (fubini theorem)..im talking about the indefinite integrals or the integrals like the one in convolution of three signals (functions) ..x(t)*y(t)*z(t).....there the limits are not defined the way we do in fubini theorem to convert a multiple integral into iterated single integrals .....

**nirax** · August 25th 2009, 04:36 AM

fubini's thm is concerned with a general measure space .. no issue of definite or indefinite (which is only in real cases) enter ... read the article in WP once.

**corleone2463** · August 25th 2009, 10:39 AM

ok thankyou nirax for ur help .... ill read the article asap ...and discuss then

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