Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2004
*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 2004

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

Search the Archive

Re: x-ArcSin[Sin[x]]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50063] Re: x-ArcSin[Sin[x]]
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Fri, 13 Aug 2004 05:56:33 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <cfcqmu$446$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <cfcqmu$446$1 at smc.vnet.net>,
 Paul Muller <paul.muller-at-epfl.ch at sicinfo2.epfl.ch> wrote:

> I am calculating the magnetic field in any point of the plane of a spire (or 
> spiral inductor). When I apply this to the center of the spire, I get the 
> following integral:
> 
> Integrate[Sin[x+ArcSin[Sin[Pi/2-x]]], {x, 0, 2Pi}]
> 
> According to textbook results for magnetic fields, the result should be 2Pi. 
> Because of the definition of ArcSin[Sin[x]] in Mathematica, the integral 
> results in Pi.
> Maybe I'm not careful enough when using the ArcSin function on the angles of
> my geometric problem (I'm an engineer, not a mathematician), but it would
> be helpful if this integral was solved "correctly".

Indeed, you are not being careful enough. If you enter

  Plot[Sin[x+ArcSin[Sin[Pi/2-x]]], {x, 0, 2Pi}]

you will see why Mathematica returns Pi for the integral. Also, if you 
enter

  FullSimplify[Sin[x+ArcSin[Sin[Pi/2-x]]], 0 < x < Pi]

you will see get the reduction you expect over the (reduced) range 
0 < x < Pi.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


  • Prev by Date: Re: Another question about Compile[]:
  • Next by Date: Re: x-ArcSin[Sin[x]]
  • Previous by thread: Re: x-ArcSin[Sin[x]]
  • Next by thread: how to graphically fill the tails of a normal distribution