# Math Help - contradict fubin's theorem

1. ## contradict fubin's theorem

can anyone give an example of a function f(x,y) for which fubini's theorem is not valid.

2. ## Re: contradict fubin's theorem

This is taken from Stewart's Calculus book

$\int_0^1 \!\!\! \int_0^1 \dfrac{x-y}{(x+y)^3}\,dx\,dy$ and $\int_0^1 \!\!\! \int_0^1 \dfrac{x-y}{(x+y)^3}\,dy\,dx$.

3. ## Re: contradict fubin's theorem

Nice example! Easy to integrate both sides and see they are not the same. I wouldn't have thought such an example would be so simple.

Of course, it doesn't "contradict Fubini's theorem". Fubini's theorem does not apply because integral does not satisfy the hypotheses.

Saurabmtz, Fubini's theorem requires that the integrand be continous on $a\le x\le b$, $c\le y\le d$ where a, b, c, and d are the limits on the appropriate integrals. This integrand is not continuous at (0, 0).