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Find the length of the curve r = cos^2(theta/2)

  1. Jun 18, 2012 #1
    Find the length of the curve r = cos^2(theta/2)

    I'm hopelessly lost.
     
  2. jcsd
  3. Jun 18, 2012 #2

    jedishrfu

    Staff: Mentor

    consider a simpler case y=x^2 and what is the length from x=0 to x=10?

    dlen = (dx*dx + dy*dy) ^ (1/2) based the pythagorian theorem

    and dy= 2xdx

    so dlen = ( dx*dx + 4x^2 dx*dx ) ^ (1/2) = (1 + 4x^2) dx

    then integrate over x to get the solution

    In your equation you must consider polar coordinates so that the dlen element is:

    dlen = ( dr^2 + (r*dtheta)^2 ) ^ (1/2)

    plugin for dr and r and integrate over theta to get the length
     
  4. Jun 18, 2012 #3
    Thanks a lot, makes more sense! Forgive my ignorance by the way.
     
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