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MathGroup Archive 2004

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Re: How to simplify to a result that is real

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50821] Re: How to simplify to a result that is real
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Wed, 22 Sep 2004 04:51:59 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <20040921115025.QQQW18891.lakermmtao10.cox.net@smtp.east.cox.net> <ciqv1p$ihc$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <ciqv1p$ihc$1 at smc.vnet.net>,
 Richard Chen <richard at doubleprime.com> wrote:

> Your procedure indeed works. However, the repeated use of
> ComplexExpand with TrigToExp sandwitched in between is hardly
> something people can come up with regularly. 
> 
> ArcTan[x,y] is indeed different from ArcTan[y/x] in general. 
> But the problem is that under our assumptions of a>b>0,0<c<Pi they
> are the same. It is the defect of the current version of mathematica
> not being able to recognize this that is the cause of the problem.
> Otherwise, the relatively simple command
> 
> FullSimplify[ComplexExpand[
> Integrate[1/(a + b Cos[t]), {t, 0, c}, 
> Assumptions -> {a > b > 0, 0 < c < Pi}], 
> TargetFunctions -> {Re, Im}], {a > b > 0, 0 < c < Pi}]
> 
> will suffice to yield the final concise result.

How about

  SetOptions[Integrate, GenerateConditions -> False]; 
  
  Simplify[Integrate[1/(a + b Cos[t]), {t, 0, c}], a > b > 0]

FullSimplify yields a slightly simpler result in terms of ArcCot instead 
of ArcTan.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 6488 2734
School of Physics, M013                         Fax: +61 8 6488 1014
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