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Intriguing Integral Illation (Posted on 2013-03-02) Difficulty: 3 of 5
Evaluate:
     1 1
    ∫ ∫ {x/y}{y/x} dxdy
    0 0
 
where {n}= n - floor(n)

No Solution Yet Submitted by K Sengupta    
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Partial answer - solution later | Comment 4 of 6 |
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
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