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 2013-03-03 02:28:51