Problem :
Let $A$ denotes region inside of $x^2 + y^2=1$.
Determine $$\iint_A \frac{1}{\sqrt{x^2+y^2}}dA$$
converge or not.
This answer says fix $y=0$ and changes double integral to single integral.
With same process, fix $y=0$.
Then our integral becomes to :
$$\int_{-1}^1 \frac{1}{|x|}dx$$
and this integral does not converge.
But, with direct calculation, polar coordinate substitution says our original double integral equals to $2\pi$.
My question is :
Is the answer what I linked above valid?
If valid, what mistake did I make?
Thanks for your help.