# Does changing the order of double integration (both integral limits are constants) alter the final answer?

I have studied that changing the order of double integration will not change the answer if both the limits of integration are constants. But this function is not agreeing with what I have studied: $$1)\int_0^1\left(\int_0^1{\frac{x-y}{(x+y)^3}dy}\right)dx$$ $$2)\int_0^1\left(\int_0^1{\frac{x-y}{(x+y)^3}dx}\right)dy$$ The answer to the first integral is 0.5 and that of the second integral is -0.5 respectively.

Can anyone please explain why is this so?

• Have you checked that the integral of the absolute value is finite? Otherwise you wouldn't be in the conditions of the Fubini theorem. – Javi Dec 7 '17 at 15:06
• $(0,0)$ is a problematic point for $\frac{x-y}{(x+y)^3}$. – Malcolm Dec 7 '17 at 15:07