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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
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Crawley WA 6009 mailto:paul at physics.uwa.edu.au
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