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Integral in cylindrical coordinates

  1. May 30, 2012 #1
    I recently did an integral of the form:

    ∫∫1/ρ dρρdθ

    the extra ρ between dρ and dθ is the cost of switching to cylindrical coordinates. Now I want to know, do you carry out the integration in ρ, keeping the ρ outside the integration (since it's technically a scaling factor that belongs to the integral in θ) or should I let it go under the integral to cancel out the ρ in the denominator?
    Obviously two different results are achieved, and I want to know which one you must do and why...
     
  2. jcsd
  3. May 30, 2012 #2
    You have to include it in the first integration, since the first integration is with respect to ρ. It cannot be treated as a constant in the first integration.
     
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