# Double integral : $\int_0^1 \int_0^1 \frac{x-y}{(x+y)^3}$

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

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?

• I know that this function is not defined on $(0,0)$, but I thought that it satisfies the Fubini's theorem, doesn't it? – Giiovanna May 10 '14 at 14:27
• 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? – Graham Hesketh May 10 '14 at 14:30