# Thread: order of integration..the core

1. ## 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...

2. 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.

3. see Fubini's theorem in wikipedia.

4. 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 .....

5. 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.

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