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MathGroup Archive 2007

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NIntegrate with change of variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77441] NIntegrate with change of variables
  • From: chuck009 <dmilioto at comcast.com>
  • Date: Sat, 9 Jun 2007 05:25:06 -0400 (EDT)

Hi,

I'm working on contour integrals using NIntegrate.  Can I specify a transformation rule that would replace both the variable of integration as well as the differential?  For example, suppose I wish to integrate f(z)dz around the unit circle, that is z=Exp[i t].  Well I could make the transformation:

NIntegrate[f[z] /. z->Exp[i t],{t,-pi, pi}] but that does not replace dz with its equivalent in terms of t, that is:

dz=i Exp[i t] dt

The correct form to integrate would be:

NIntegrate[f[Exp[i t]] i Exp[i t],{t,-pi, pi}]

Is there a way to define a transformation rule that would make both those substitutions for unspecified z=g(t)?


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