This is a sequel of the question posted some hours ago: Is this integral finite? (convergent)
Let us consider $\mathbb{R}^2$ and only the region $R=\{(x,y)\in \mathbb{R}^2: \, |x|>1, |y|>1\}$. Is the following integral finite for any value of $\beta>0$?
$$\int_{R} \frac{1}{(\max \{|x|,|y|\})^\beta} dxdy.$$
For $\beta \leq 2$ we saw that it is inifinite by the previous post. But can we now find a suitable power to make it finite? :)
Here is a graph of the integrand for $\beta=4$, it looks convergent but of course I'm not sure. http://www.livephysics.com/tools/mathematical-tools/online-3-d-function-grapher/?xmin=-100&xmax=100&ymin=-100&ymax=100&zmin=Auto&zmax=Auto&f=1%2F%28%28max%28abs%28x%29%2Cabs%28y%29%29%29%5E4%29 Any ideas? :) Thanks a lot :)