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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