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MathGroup Archive 2001

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Re: Weird trigonometric integral and Simplification question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31783] Re: Weird trigonometric integral and Simplification question
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
  • Date: Sun, 2 Dec 2001 04:24:56 -0500 (EST)
  • References: <9ua41r$19f$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Bruce Atwood <bta at attewode.com> wrote:
> Message 1: Weird trigonometric integral
>
> The function Sqrt[1-Cos[t]] is continuous for all real t. Hence its
> integral must be continuous for all real t. In fact there is a general
> solution that is continuous for all real t.

Yes, for example,
2*Sign[Sin[t]]*(Sqrt[2]-Sqrt[Cos[t]+1]) + 4*Sqrt[2]*Floor[t/(2*Pi)+1/2]
is a continuous antiderivative.

> However Mathematica gives only a "particular" solution that is only
> true on the interval (0, 2 Pi).

That's not quite accurate. Mathematica's antiderivative is continuous on
all intervals of the form (2*N*Pi, 2*(N+1)*Pi), for integer N. But that
doesn't alter the point of your question, after all.

> Is there any way to know in advance when to expect these subtle and
> difficult problems?

Good question.

   David Cantrell

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