I'm trying to show that
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
I guess it does not really make any difference in the end because the right hand sides of both of the equalities are .
But which one is right??
First, because of the absolute value, the obvious thing to do is to write this as two integrals. As long as 0< y< x, the fraction is postive:
and as long as 0< x< y, the fraction is negative:
Then do as Prove It suggested, convert to polar coordinates:
The line x= 1 is given by so
The original integral is the sum of those, of course.