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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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Some Thoughts re: Just guessing -- numerical integration comparison | Comment 2 of 6 |
(In reply to Just guessing by Steve Herman)

DECLARE FUNCTION frac# (x#)
DEFDBL A-Z
OPEN "intintil.txt" FOR OUTPUT AS #2
incr = .00001#: incr2 = incr * incr
FOR y = incr / 2 TO 1 STEP incr
    FOR x = incr / 2 TO 1 - incr / 2 STEP incr
        sum = sum + frac(x / y) * frac(y / x) * incr2
        sum2 = sum2 + x * y * incr2
    NEXT x
NEXT y
PRINT sum, sum2
PRINT #2, sum, sum2

FUNCTION frac (x)
frac = x - INT(x)
END FUNCTION

finds the integral asked for as .1775330530819235 while the guess integrates to .2499999999991424 which looks like it's 1/4.


  Posted by Charlie on 2013-03-02 14:49:35
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