Re: HoldAll for Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg97978] Re: HoldAll for Integrate*From*: dh <dh at metrohm.com>*Date*: Fri, 27 Mar 2009 05:33:40 -0500 (EST)*References*: <gqfknb$kht$1@smc.vnet.net>

Hi Tammo, what Integrate really does can only somebody from Wolfram explain. But it completely eludes me why the integration variable in "Integrate" is not localized. Maybe some can give a reason for this. For the rest of us, we may define a new Integrate that does localize and see if it creates troubles. Here is a possibility, where we use Hold and Replace to protect the variable by giving it another name: SetAttributes[myInt, HoldAll]; myInt[integ_, {var_, low_, high_}] := Module[{integ0, var0}, Integrate @@ (Hold[integ, {var, low, high}] /. HoldPattern[var] -> var0) ]; Here is another one using "With" to protect the integration variable: SetAttributes[myInt, HoldAll]; myInt[integ_, {var_, low_, high_}] := With[{var = Unevaluated@var}, Integrate[integ, {var, low, high}]]; Daniel Tammo Jan Dijkema wrote: > 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 > >