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MathGroup Archive 2004

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Re: Another Integrate error

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52594] Re: Another Integrate error
  • From: "snoofly" <snoofly at snoofly.com>
  • Date: Fri, 3 Dec 2004 03:54:07 -0500 (EST)
  • References: <comgts$9gn$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

5.1 calculates both Out[2] and Out[3] as 1

"Ray Koopman" <koopman at sfu.ca> wrote in message 
news:comgts$9gn$1 at smc.vnet.net...
> This is a bivariate normal probability density:
>
> In[1]:= f[x_,y_,r_] = Exp[(x^2 + y^2 - 2*r*x*y)/(r^2 - 1)] /
>                      (Pi Sqrt[1 - r^2]);
>
> It should integrate to 1:
>
> In[2]:= Integrate[f[x,y,r],{x,-Infinity,Infinity},{y,-Infinity,Infinity}]
> Out[2]= 0
>
> In[3]:= Integrate[f[x,y,r],{x,-Infinity,Infinity},{y,-Infinity,Infinity},
>                  Assumptions -> {Element[r,Reals], -1 < r < 1}]
> Out[3]= 1
>
> In this case I happened to know that the integal should be 1,
> but what about more obscure cases?
> When can I believe a result from Integrate?
>
> In[4]:= $Version
> Out[4]= 5.0 for Mac OS X (November 19, 2003)
> 


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