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 -- -------------------- http://NewsReader.Com/ -------------------- Usenet Newsgroup Service