[TS 23099]--Re:integrals

[Hans.Dolhaine@XXXXXXX.com]

Guten Tag allerseits,

zur Kenntnis eine Korrespondenz mit support.

Mit freundlichen Grüssen

Hans Dolhaine
_________________________________

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----- Weitergeleitet von Hans Dolhaine/KGaA/HENKEL am 22.10.2003 14:23
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                      support@wolfram.c                                                                                 
                
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From: Hans.Dolhaine@XXXXXXX.com
Date: Wed, 15 Oct 2003 11:28:20 +0100
Subject: integrals
To: support@XXXXXXX.com

hello to you,

I encountered a problem which may be a bug, but  I'm not quite sure. Gauss
states, that integrals over surfaces may be transfomed to integrals over
volumes according to

surfaceintegral  [  a . dS  ]  =  volumeintegral  [  div . a  dV   ]

Please have a look at the attached notebook. I have a vector aa whose
divergence simplifies to 1/r, so the volumeintegral (over the whole sphere)
is rather simple). Trying to do the surfaceintegral yields a result which
is quite different. When I try numerical  integration I get a warning that
the integrand(s) is (are) singlular at some points and no evaluation takes
place. That is ok. But the symbolic integration, if the sequence of doing
the integrals is chosen appropriately, gives without any complaints some
values. Generally I trust these, but this seems to be a bug: no reference
to the possible singularities is given and the final result is totally
different from the volumeintegral.

Is this a bug or have I overlooked something?

Kind regards

Hans Dolhaine

(See attached file: support.nb)
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VTR-TS
Phone:      +49-211-797-4809
Fax:        +49-211-798-1853
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E-Mail:     Hans.Dolhaine@XXXXXXX.com

=======================================================

Hello,

Thank you for taking the time to send us this report.

You are correct that some of the results from Integrate
in your example are wrong.  In particular, the result
from each of the last three Integrate examples in the
notebook that was included with your message should be
2Pi/3.  This can be verified using numerical integration.

In[]:= 2 Pi NIntegrate[Evaluate[i1[[1]] /. R -> 1],
           {t, 0, Pi/2, Pi}, SingularityDepth -> 999]

Out[]= 2.0944

In[]:= NIntegrate[Evaluate[i1[[2]] /. R -> 1],
             {p, 0, Pi, 2 Pi}, {t, 0, Pi/2, Pi}]

Out[]= 2.0944

In[]:= NIntegrate[Evaluate[i1[[3]] /. R -> 1],
               {p, 0, 3, 2 Pi}, {t, 0, Pi/2, Pi}]

Out[]= 2.0944

The behavior of these examples in the current version
of Mathematica (Version 5.0) has changed, but remains
incorrect.  I have filed these examples so that this
behavior can be investigated.

I have not reviewed the mathematics or the analysis
that you described, and do not know if that analysis
is correct.

Unfortunately, there are no known workarounds for this
error in the Integrate function.  We apologize for any
difficulties caused by this error.

Technical Support
Wolfram Research


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