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MathGroup Archive 2003

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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)         
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Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul



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