Originally Posted by

**willy0625** I'm trying to show that

$\displaystyle \int\int_{0\leq x,y\leq 1}\Bigg\vert\frac{x^2-y^2}{(x^2+y^2)^2}\Bigg\vert\hspace{1mm}dxdy = 2\int_{0}^{1}\int_{0}^{1}\frac{x^2-y^2}{(x^2+y^2)^2}dxdy$

so that I can use Fubini's theorem to deduce that the iterated integrals of the integrand(without the absolute value function) are not the same.

But I got

$\displaystyle \int\int_{0\leq x,y\leq 1}\Bigg\vert\frac{x^2-y^2}{(x^2+y^2)^2}\Bigg\vert\hspace{1mm}dxdy = 2\int_{0}^{1}\int_{0}^{1}\frac{x^2-y^2}{(x^2+y^2)^2}dxdy + \frac{\pi}{4}_{.}$

I guess it does not really make any difference in the end because the right hand sides of both of the equalities are $\displaystyle \infty$.

But which one is right??