All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Intriguing Integral Illation (Posted on 2013-03-02)
Evaluate:
```     1 1
∫ ∫ {x/y}{y/x} dxdy
0 0

where {n}= n - floor(n)
```

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 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
Please log in:
 Login: Password: Remember me: Sign up! | Forgot password

 Search: Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information