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Green's theorem - area of a cycloid

  1. Apr 17, 2014 #1
    1. The problem statement, all variables and given/known data

    Use Green’s Theorem to find the area of the region between the x – axis and one arch of the cycloid
    parameterized by p(t) = < t-2sin(t),2-2cos(t)> for 0≤t≤2∏

    2. Relevant equations

    3. The attempt at a solution
    My problem here is that I get different answers depending on if I use
    F=<0,x> or F = <-y,0>

    The 8∏ answer that I have to the right is the correct one. How do I know which force field to pick?

    Last edited: Apr 17, 2014
  2. jcsd
  3. Apr 17, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper

    You can pick either one. The only problem is that you did the first integral wrong. The integral of t*sin(t) between 0 and 2pi isn't zero.
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