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Homework Help: Length of a curve

  1. Nov 1, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the length of the curve.

    x=cos(2t)
    y=sin(3t)
    0≤t≤2∏

    I know the length is just the integral from 0 to 2∏of the magnitude of the velocity.


    3. The attempt at a solution

    x'=-2sin(2t) x'^2=4sin^2(2t)
    y'=3cos(3t) y'^2=9cos^2(3t)

    c=∫√4sin^2(2t)+9cos^2(3t)

    Im having trouble evaluating the integral. Could some please point me in the right direction?

    Thanks
     
  2. jcsd
  3. Nov 1, 2011 #2

    HallsofIvy

    User Avatar
    Science Advisor

    [itex]4sin^2(3t)+ 9cos^2(3t)= 4sin^2(3t)+ 4cos^2(3t)+ 5cos^2(3t)= 4+ 5cos^2(3t)[/itex]. Let [itex]u= 4+ 5cos^2(3t)[/itex].
     
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