MathGroup Archive 1997

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

Search the Archive

Incorrect definite integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg9468] Incorrect definite integral
  • From: Josip Loncaric <josip at icase.edu>
  • Date: Thu, 6 Nov 1997 02:40:12 -0500
  • Organization: ICASE
  • Sender: owner-wri-mathgroup at wolfram.com

Mathematica 3.0 makes a curious mistake in the following evaluation.

  f[k_,x_,y_] := 2*Sinh[x]*Cos[k*y]/(Cosh[x]-Cos[y])

  d[k_,x_] := Integrate[f[k,x,y],{y,0,Pi}]/(2*Pi)

  i[k_,x_,y_] := Integrate[f[k,x,y],y]/(2*Pi)

For positive x, the definite integral d[k,x] should evaluate to an
expression equivalent to E^(-Abs[k]*x).  Mathematica obtains the
correct result EXCEPT when Abs[k]=1, when d[1,x] and d[-1,x] return

  -Sinh[x]

which is quite wrong.  By contrast, the indefinite integral i[1,x,y] is

  (2*ArcTan[Coth[x/2]*Tan[y/2]]*Cosh[x] - y*Sinh[x])/Pi

which smoothly varies from 0 at y=0 to E^(-x) as y->Pi from below, as it
should.  

Mathematica's definite integral gets a wrong answer because it
apparently selects the wrong direction in taking the limit y->Pi.  Why
anyone would approach the upper limit from ABOVE when the integrand
need not even be defined outside the bounds of integration is puzzling.


 
-- 
Dr. Josip Loncaric, Senior Staff Scientist ICASE, M/S 403, NASA Langley
Research Center, Hampton, VA 23681-0001 Phone: (757) 864-2192          
mailto:josip at icase.edu Fax:   (757) 864-6134                  
http://www.icase.edu/~josip/


  • Prev by Date: Error in integrals?
  • Next by Date: Re: Lists and Recursion
  • Previous by thread: Re: Re: Error in integrals?
  • Next by thread: Postscript Files