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HoldAll for Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97923] HoldAll for Integrate
  • From: Tammo Jan Dijkema <T.J.Dijkema at gmail.com>
  • Date: Thu, 26 Mar 2009 05:18:07 -0500 (EST)

The following commands yield unexpected output:

x=10;
Integrate[x^2, {x,0,1}]

That is because Integrate does not have attributes HoldAll, so that the 
second command will be interpreted as Integrate[100, {10,0,1}] which is 
not a command that Integrate can work with (so a warning message is 
returned).

However, I can add the attribute HoldAll to Integrate myself:

SetAttributes[Integrate, HoldAll];

I'm not very sure what to expect when now trying the same experiment 
(the correct answer 1/3 would be nice), but the actual output surprised 
me:

x=10;
Integrate[x^2, {x,0,1}]

Yields as output: 0 (without any warnings). Could anyone explain why I 
should have expected this result?

On a side note, I found a similar in the Tech Support column of the 
Mathematica Journal Volume 6, Issue 2, by Carl Roy. He tried the 
integral without limits:

x=10;
SetAttributes[Integrate, HoldAll];
Integrate[x^2, x]

In the journal, the output 1000/3 is mentioned, whereas in Mathematica 
7.0.1 this outputs 1000.

Again, does anyone understand this?

Regards,

Tammo Jan Dijkema



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