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Problem with change of variables in an integral
Posted:
Sep 3, 2013 11:33 PM


Hello,
Although I know how to make a change of variables in an integral I can only do it manually by applying a substitution rule to the integrand and the differential e.g {f[z],\[DifferentialD]z}//. {z> r E^(I \[Phi]),\[DifferentialD]z>E^(I \[Phi]) \[DifferentialD]r,\[Phi] > (2\[Pi])/3}
But it cannot applied this substitution rule directly to the integral, e.g. Integrate[f[z],{z,0,\[Infinity]}] //. {z> r E^(I \[Phi]),\[DifferentialD]z>E^(I \[Phi]) \[DifferentialD]r,\[Phi] > (2\[Pi])/3}
Comparing with the correct result, the exponential factor E^((2 I \[Pi])/3) = (1)^(2/3) is missing in the evaluation of the integral. The correct appearance of the integral is : Integrate[1/(1+r^3) E^((2 I \[Pi])/3),{r,0,\[Infinity]}]
How can I force Mathematica (V8) to perform the correct transformation of variables as regards to the integral (and not to its separate parts of it as {f[z],\[DifferentialD]z} ?
Any suggestions are appreciated. Robert Kragler
 Robert Kragler Email : kragler@hsweingarten.de URL : http://portal.hsweingarten.de/web/kragler



