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