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        riddles >> general problem-solving / chatting / whatever >> What a result!
        
(Message started by: BNC on Sep 29^th, 2003, 3:46pm)

Title: What a result!
Post by BNC on Sep 29^th, 2003, 3:46pm

Solve this integral (analytical, not numerical solution) to reveal its mysteries...

int(0,1,[x^4*(1-x)^4/(1+x^2)]dx)

Title: Re: What a result!
Post by towr on Sep 30^th, 2003, 12:21am

heh, cute

Title: Re: What a result!
Post by Sir Col on Sep 30^th, 2003, 10:04am

Could you clarify, BNC; is it x^4*(1-x)^(4/(1+x^2)) or is it (x^4*(1-x)^4)/(1+x^2)?

Title: Re: What a result!
Post by towr on Sep 30^th, 2003, 10:24am

the latter..
(it'd be rather more difficult to solve otherwise)

Title: Re: What a result!
Post by Sir Col on Sep 30^th, 2003, 10:39am

I rather hoped that was the case; I wouldn't know where to start on the former. In which case... very clever, BNC. How do you discover these results? All we need now is one for 355/113. ;)

Title: Re: What a result!
Post by BNC on Sep 30^th, 2003, 11:43am

I've heard people say that you could define a mathematician to be someone who finds this result delightful...

Origin: "Pancake functions and approximations to pi" , The Mathematical Gazette, Vol 79, Number 485, July 1995 pp371-374, which won an award for the best Note in 1995.

Note: The integrand is called "a pancake function" because it's very, very flat in [0,1]. Maybe even flater than Kansas :P

Title: Re: What a result!
Post by THUDandBLUNDER on Sep 30^th, 2003, 10:33pm

Quote:

Maybe even flater than Kansas

http://www.guardian.co.uk/life/feature/story/0,13026,1048791,00.html

Title: Re: What a result!
Post by BNC on Oct 1^st, 2003, 1:28am

It was discussed here (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1060173107;start=33) (search for a post by Icarus). That's why I mentioned it in the first place... to tease him.