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MathGroup Archive 1998

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Re: FresnelS & FresnelC

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13823] Re: FresnelS & FresnelC
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Sat, 29 Aug 1998 04:41:04 -0400
  • Organization: University of Western Australia
  • References: <6s5mf7$cc5@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Steven T. Hatton wrote:
> 
> I copied directly from *Mathematica By Example* in PDF format, pg 220,
> Revised First Ed..   I do not get the same result as the author.  Does
> any body else get ~pi ?  I get 1.24012 for the numerical result, and
> the same thing the book says for the symbolic result.
> 
> IN[ ]= value=Integrate[Cos[x^2-y^2],{x,0,Sqrt[Pi]},{y,0,Sqrt[Pi]}]
> 
> OUT [ ]=  (Pi (FresnelC[Sqrt[2]]^2 +  FresnelS[Sqrt[2]]^2 )) / 2
> 
> IN[ ]= N[value]
> 
> OUT[ ]= 3.14159

I don't have Mathematica By Example (nor the PDF version).  However, the
values you obtain for the symbolic and numeric integration are
consistent:

In[1]:= value=Integrate[Cos[x^2-y^2],{x,0,Sqrt[Pi]},{y,0,Sqrt[Pi]}]
Out[1]=
	1                      2                    2
	- Pi (FresnelC[Sqrt[2]]  + FresnelS[Sqrt[2]] )
	2

In[2]:= N[value]
Out[2]= 1.24012

In[3]:= NIntegrate[Cos[x^2-y^2],{x,0,Sqrt[Pi]},{y,0,Sqrt[Pi]}] Out[3]=
1.24012

Cheers,
	Paul 

____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907       
mailto:paul at physics.uwa.edu.au  AUSTRALIA                       
http://www.physics.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________


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