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) >