Re: Bug with Integrate in v7?
- To: mathgroup at smc.vnet.net
- Subject: [mg103139] Re: [mg103116] Bug with Integrate in v7?
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Wed, 9 Sep 2009 04:42:32 -0400 (EDT)
- Reply-to: hanlonr at cox.net
I see the same result on my system
$Version
7.0 for Mac OS X x86 (64-bit) (February 19, 2009)
For other cases where the order of integration is important, you should note that the two cases that you gave have different orders of integration. The iterator for the outer most integration comes first inside a multiple integration. However, in this case the order is not the cause of the problem.
Bob Hanlon
---- kostka <kostka at gmail.com> wrote:
=============
Okay it took me an hour to track this down, and the only explanation I
can see is that there is a bug in Mathematica v7 with Integral[] with
multiple bounds.
In v7.0 (answers should both be 512/27, only one of them is):
In[1]:= f = (x - 1)^2*(y - 1)^2*(z - 1)^2;
Integrate[f, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}]
Integrate[Integrate[Integrate[f, {x, -1, 1}], {y, -1, 1}], {z, -1, 1}]
Out[2]= 0
Out[3]= 512/27
In v6.0 (correct behavior):
In[1]:= f = (x - 1)^2*(y - 1)^2*(z - 1)^2;
Integrate[f, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}]
Integrate[
Integrate[Integrate[f, {x, -1, 1}], {y, -1, 1}], {z, -1, 1}]
Out[2]= 512/27
Out[3]= 512/27
Serious bug, right? Or am I missing something obvious?
Tim