It is asked to calculate

$$\int_0^1 \int_0^1 \frac{x-y}{(x+y)^3}dxdy \; and \; \int_0^1 \int_0^1 \frac{x-y}{(x+y)^3}dydx$$

and find the relation between my answer and Fubini's theorem.

But for the first integral I got $-\frac{1}{2}$ and the second $\frac{1}{2}$. I thought the integrals should gave the same answer, but I couldnt figure out what I was doing wrong.

Can someone give me a help?

Thanks in advance!

  • 3
    $\begingroup$ If the results are not the same and Fubini theorem states that under some given hypothesis the results are the same, this means that... $\endgroup$ – Did May 10 '14 at 14:24
  • 1
    $\begingroup$ I know that this function is not defined on $(0,0)$, but I thought that it satisfies the Fubini's theorem, doesn't it? $\endgroup$ – Giiovanna May 10 '14 at 14:27
  • 1
    $\begingroup$ Pure logic says it cannot. Why did you think etc.? $\endgroup$ – Did May 10 '14 at 14:28
  • 1
    $\begingroup$ Continuity is not even a hypothesis of Fubini. And Fubini has other hypotheses. $\endgroup$ – Did May 10 '14 at 14:30
  • 4
    $\begingroup$ With regards to expecting the result to be the same in both integrals, what happens if you just rename the variable $y$ as $x$ and the variable $x$ as $y$ in the second integral and then compare it to the first? $\endgroup$ – Graham Hesketh May 10 '14 at 14:30

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