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Math Help - Green's theorem

  1. #1
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    Green's theorem

    Mods | Mathematical Institute - University of Oxford

    paper D, 2008
    question 4b

    I really cant see where to start, but I guess it's a fairly standard Green's theorem result.. the squares are putting me off alot

    could someone please show me how to do it.

    many thanks
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  2. #2
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    Quote Originally Posted by James0502 View Post
    Mods | Mathematical Institute - University of Oxford

    paper D, 2008
    question 4b

    I really cant see where to start, but I guess it's a fairly standard Green's theorem result.. the squares are putting me off alot

    could someone please show me how to do it.

    many thanks
    Using Green's theorem you want to calculate

    \frac{1}{2}\int_0^{2\pi} x dy - y dx where

     x = 4 \cos \phi - \cos 4 \phi,\;\;y = 4 \sin \phi - \sin 4 \phi
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    Note x dy - y dx simplifies very nicely!
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    sorry.. I still dont understand.. How have they found the first result for example?

    the 'show that' bit...

    with (dT/dx)^2 + (dT/dy)^2

    many thanks
    and what is an epicycloid?

    what is the standard result for finding the area of it?
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