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)?