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Understanding what integrating in polar gives you

  1. Apr 1, 2012 #1
    I am not understanding integration with polar coordinates, or at least visualizing what is happening. Here's the integral calculated in Wolfram:


    the integral before I changed it to polar was just ∫R(x2-y2)dA where R is the first quadrant region between the circles of radius 1 and 2

    mathematically it makes sense that the answer is 0.

    but when you draw the picture it is a quarter of a washer in the xy plane. This does not seem like 0 to me. Would someone please explain where my thinking is going wrong?


    First post:smile:
  2. jcsd
  3. Apr 1, 2012 #2


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    The function x^2 -y^2 is symmetric in that region when you reflect over the line x=y, with the function negative on one half and positive on the other
  4. Apr 1, 2012 #3
    ok that makes sense, but why the line x=y?
  5. Apr 1, 2012 #4


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    Think about the nature of ^2 term in terms of the solutions (hint: + and -).
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