Re: Problem with change of variables in an integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg131626] Re: Problem with change of variables in an integral*From*: Youngjoo Chung <ychung12 at gmail.com>*Date*: Fri, 13 Sep 2013 00:35:35 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <l0mio3$ltf$1@smc.vnet.net>

Dear Alexei, I believe the references mentioned in Alex's reply below explains the evaluation procedure well. In your earlier message, with f[z_] := 1/(1 + z^3); Integrate[...] is evaluated to (2 \[Pi])/(3 Sqrt[3]) before being passed to Map. This explains the difference that you saw. If f[z] is not known, Integrate cannot evaluate and is passed to Map as is as shown in your message. However, the following code Clear[f, \[Phi]]; Map[ReplaceAll[#, {z -> r*Exp[I \[Phi]], \[Phi] -> 2 \[Pi]/3}] &, Integrate[f[z], {z, 0, \[Infinity]}]] % /. f[z_] -> z issues an error message Integrate::ilim: Invalid integration variable or limit(s) in {E^(I \[Phi]) r,0,\[Infinity]}. >> and even though f[z_] = z is integrable, integration will not be done since E^(I \[Phi]) is not a valid integration variable. Sincerely, Youngjoo