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Find The Region

  1. Apr 14, 2009 #1
    Find the region enclosed by one leaf of the function r=2 sin2θ

    Now i know how the diagram looks like for this function.
    The diagram can be obtained by using :

    x= r cosθ = 2 sin2θ cosθ
    y= r sinθ = 2 sin2θ sinθ

    Now i have to find the region enclosed by one of the leaves which i am not able to do.
    I know i have to use the jacobian and also that i can use the above as cylindrical coordinates but what do i integrate? i dont know which function to integrate.

    Any Suggestions for that??

    thank you
  2. jcsd
  3. Apr 14, 2009 #2
    [tex]\frac{1}{2}\int r^{2} .d\theta[/tex]

    You can use that formula
  4. Apr 14, 2009 #3


    User Avatar

    Staff: Mentor

    Wouldn't it be [tex]\int r d\theta[/tex]

    I could be missing something of course...
  5. Apr 15, 2009 #4
    Is the half for finding each half of the region of the leaf?
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