Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Indefinite integration problem on ArcTanh(f(Cos))

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69982] Re: Indefinite integration problem on ArcTanh(f(Cos))
  • From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
  • Date: Thu, 28 Sep 2006 06:17:54 -0400 (EDT)
  • References: <efdks2$12a$1@smc.vnet.net>

"ANDREW PALFREYMAN" <andrew_ppp at hotmail.com> wrote:
> Hi.
> I'm integrating Sin[t] / (1 + k Cos[2t]) , over 0 < k < 1, using
> Mathematica 4.1. I'm plotting spot values k=0.1, 0.8, 0.95 over  0 < t <
> 10.
>
> This represents the acceleration of a charged particle in an alternating
> electric field, where k represents a particular modulation of its
> effective inertia. Although the velocity plots (the integral dt) look
> fine (symmetrical about zero), the plots for position (integrating
> velocity dt) are clearly wrong; I get a massive expression (about 20
> lines!) which will not differentiate successfully back to the original
> velocity expression, and they are decidedly asymmetrical about zero. The
> position plot ought to look like a sinewave as k->0, but there's no
> resemblance.

I don't know what answer version 4.1 gives, but the current version's
answer seems to be correct. Did you think of trying The Wolfram Integrator

<http://integrals.wolfram.com/index.jsp> ?

It's free and gives the same result for the indefinite integral as the
current version of Mathematica.

Anyway, if 0 < k < 1, perhaps the nicest way to write the antiderivative is

- ArcTan[Sqrt[2k/(1-k)] Cos[t]] / Sqrt[2k(1-k)].

David


  • Prev by Date: Re: Indefinite integration problem on ArcTanh(f(Cos))
  • Next by Date: plot questions
  • Previous by thread: Re: Indefinite integration problem on ArcTanh(f(Cos))
  • Next by thread: Re: Indefinite integration problem on ArcTanh(f(Cos))