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I Limits of integration on Polar curves

  1. Mar 6, 2017 #1
    General question, how do you determine the limits of integration of a polar curve? Always found this somewhat confusing and can't seem to find a decent explanation on the internet.
     
  2. jcsd
  3. Mar 6, 2017 #2

    BvU

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    What's a polar curve ? A circle on the South pole ? A trajectory described in polar coordinates ?
    Please give a clearer description.
     
  4. Mar 6, 2017 #3
    Oh sorry, any closed curve defined in Polar coordinates. Cardiods, limacons, circles, the works.
     
  5. Mar 6, 2017 #4

    BvU

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    I should have asked straight away too: What is it you want to integrate ? some function over the surface, over the boundary ? A vector function ? Just the circumference or the area ?
     
  6. Mar 7, 2017 #5
    The area enclosed by the Polar curve using Int(1/2 r^2) d theta. I find the determination of the limits of integration slightly ambiguous when I watch any tutorials or read up on Polar coordinates. I normally just use graph trace but I'd like to get an intuitive understanding
     
  7. Mar 7, 2017 #6

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    Browsing some of the links at the lower left might be instructive.
    We did a cardioid here not so long ago (no full solution, just hints).
    Point is: with a concrete example we can see where things go wrong for you.
    As you can see in the link, I am an advocate of your approach:
    and from that, with experience, grows intuition. The latter two aren't sold by weight (in contrast with what some managers seem to think).

    I don't think I can provide much guidance based on e.g.
    All I can say is usually ##\theta## runs from 0 to ##2\pi## or from ##-\pi## to ##+\pi##. But I doubt if that is helpful for you.
     
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