# order of integration..the core

• Aug 25th 2009, 05:00 AM
corleone2463
order of integration..the core
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...
• Aug 25th 2009, 05:03 AM
Prove It
Quote:

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.
• Aug 25th 2009, 05:18 AM
nirax
see Fubini's theorem in wikipedia.
• Aug 25th 2009, 05:27 AM
corleone2463
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 .....
• Aug 25th 2009, 05:36 AM
nirax
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.
• Aug 25th 2009, 11:39 AM
corleone2463
ok thankyou nirax for ur help .... ill read the article asap ...and discuss then