S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Sun, 20 Apr 2014 09:15:00 UTC

All times are UTC [ DST ]




Post new topic Reply to topic  [ 10 posts ] 
Author Message
 Post subject: Re: cool integral
PostPosted: Fri, 25 Jul 2008 03:05:49 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame

Joined: Sat, 18 Mar 2006 08:42:24 UTC
Posts: 834
cody wrote:
Give this one a go:

$ I=\int_{0}^{1}\int_{0}^{1}\frac{1}{\ln(xy)(1+(xy)^{2})}dxdy



Spoiler:
in the inner integral put xy=v. then:

$ I=\int_0^1 \int_0^y \frac{dv \ dy}{y(1 + v^2)\ln v}=\int_0^1 \int_v^1 \frac{dy \ dv}{y(1+v^2) \ln v }=-\int_0^1 \frac{dv}{1+v^2}=-\frac{\pi}{4}. \ \ \  \square


Top
 Profile  
 
 Post subject:
PostPosted: Sat, 26 Jul 2008 06:28:44 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame

Joined: Sat, 18 Mar 2006 08:42:24 UTC
Posts: 834
here's a "cool" integral: $ \int_0^{\frac{\pi}{2}} x\ln(\sin x) \ dx = ?

Hint:
Spoiler:
the answer is in terms of \zeta(3).


Top
 Profile  
 
 Post subject:
PostPosted: Wed, 30 Jul 2008 16:57:36 UTC 
Offline
S.O.S. Oldtimer

Joined: Sun, 8 Jun 2008 01:27:21 UTC
Posts: 173
Location: Pennsylvania
Sorry for not getting back to you on MHF Galctus...I have been up for 39 hours and I jsut forgot! Sorry...but let me pose this question for Commutative...do you mean to solve this by use of the power series of arcsine squared with reciprocated central binomial coefficients etc? Or is there an easier way?


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 10 posts ] 

All times are UTC [ DST ]


Who is online

Users browsing this forum: No registered users


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
cron
Contact Us | S.O.S. Mathematics Homepage
Privacy Statement | Search the "old" CyberBoard

users online during the last hour
Powered by phpBB © 2001, 2005-2011 phpBB Group.
Copyright © 1999-2013 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA