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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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