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Double integral using polar coordinates

  1. Nov 9, 2012 #1
    The question is in the paint document

    I wanted to know why they integrated from 0 to pi and not from 0 to 2pi
     

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  2. jcsd
  3. Nov 9, 2012 #2

    LCKurtz

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    Draw a picture of the region.
     
  4. Nov 9, 2012 #3
    There that is the region I believe
     

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  5. Nov 9, 2012 #4
    Sorry I just looked at the question again.. it said above the x-axis
     
  6. Nov 9, 2012 #5

    LCKurtz

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    So does that answer your question?
     
  7. Nov 9, 2012 #6
    One last question. When is it best to use polar coordinates rather than spher. coord. For instance if I integrating a cylinder I would use polar and If I was integrating a cone or a ellipsoid I should use spher. coord. But what about elliptical parabaloids or eliptic hyperbolas of one or two sheets?
     
  8. Nov 9, 2012 #7
    To answer my above question (post # 6) I am guessing is depends on my region on the xy plane that I am integrating over..
     
  9. Nov 9, 2012 #8

    LCKurtz

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    You have the right general division of the methods. Sometimes they overlap though. A paraboloid would suggest cylindrical coordinates for the elliptical cross section but rectangular if you were doing one of the other cross sections. Similarly for the hyperboloids.
     
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