Re: integrat trig radical
- To: mathgroup at smc.vnet.net
- Subject: [mg39607] Re: integrat trig radical
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Wed, 26 Feb 2003 02:41:24 -0500 (EST)
- Organization: The University of Western Australia
- References: <b3ck48$7vs$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <b3ck48$7vs$1 at smc.vnet.net>, Friedrich Laher <mathefritz at schmieder-laher.de> wrote: > is there any mathematical reason for mathematica, not 1st internally > using Cos[x/2] = Sqrt[(1 + Cos[x])/2] before integrating Sqrt[1 + Cos[x]] ? Compare FullSimplify[Cos[x/2] - Sqrt[(1/2) (1 + Cos[x])], 0 < x < Pi] with FullSimplify[Cos[x/2] - Sqrt[(1/2) (1 + Cos[x])], Pi < x < 2 Pi] > It even refuses to answer True to > Integrate[Sqrt[1 + Cos[x]],x] == 2*Sqrt[2]*Sin[x/2] Compare FullSimplify[Integrate[Sqrt[Cos[x] + 1], x], 0 < x < Pi] with FullSimplify[Integrate[Sqrt[Cos[x] + 1], x], Pi < x < 2 Pi] Cheers, Paul -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul