Another Integrate error

*To*: mathgroup at smc.vnet.net*Subject*: [mg52573] Another Integrate error*From*: koopman at sfu.ca (Ray Koopman)*Date*: Thu, 2 Dec 2004 02:21:45 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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)

**Follow-Ups**:**Re: Another Integrate error***From:*DrBob <drbob@bigfoot.com>