Evaluate:
1 1
∫ ∫ {x/y}{y/x} dxdy
0 0
where {n}= n  floor(n)
It's late at night but I'll share what I have
If you change the limits of the integrations from .5 to 1 you get the exact solution
(ln4 1)/8
When I get a chance I'll look at the rest of the portion between y=2x and x=2y.
Then it shouldn't be too hard to figure out how to get the portions between x=2y and x=3y and x=4y etc.
And then finally sum them up.
Looking at Daniel's solution it seems odd that pi will come up. But pi has a way of doing that.

Posted by Jer
on 20130303 02:28:51 