Re: FresnelS & FresnelC

• To: mathgroup at smc.vnet.net
• Subject: [mg13845] Re: [mg13809] FresnelS & FresnelC
• From: BobHanlon at aol.com
• Date: Sat, 29 Aug 1998 04:41:20 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```value=Integrate[Cos[x^2-y^2],{x,0,Sqrt[Pi]},{y,0,Sqrt[Pi]}]

1/2*Pi*(FresnelC[Sqrt[2]]^2 + FresnelS[Sqrt[2]]^2)

N[value]

1.24012

NIntegrate[Cos[x^2-y^2],{x,0,Sqrt[Pi]},{y,0,Sqrt[Pi]}]

1.24012

Plot3D[Cos[x^2-y^2],{x,0,Sqrt[Pi]},{y,0,Sqrt[Pi]}];

Since you are integrating over a region whose area is Pi and the maximum
value of the function is one, then the integral is clearly less than
Pi.

Bob Hanlon

In a message dated 8/28/98 9:12:23 AM, hattons at cpkwebser5.ncr.disa.mil
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

```

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