Re: Another Integrate error

• To: mathgroup at smc.vnet.net
• Subject: [mg52578] Re: Another Integrate error
• From: DrBob <drbob at bigfoot.com>
• Date: Fri, 3 Dec 2004 03:53:30 -0500 (EST)
• References: <200412020721.CAA05858@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Both integrals give 1 in version 5.1.

>> When can I believe a result from Integrate?

When you've double-checked it, possibly with NIntegrate.

Bobby

On Thu, 2 Dec 2004 02:21:45 -0500 (EST), Ray Koopman <koopman at sfu.ca> wrote:

> 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)
>
>
>
>

--
DrBob at bigfoot.com
www.eclecticdreams.net

```

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