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Computing Arc Length and Cannot Solve the Integral

  1. Feb 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the length of the polar curve.

    Complete the cardioid r=1+cosθ

    2. Relevant equations

    L=∫αβ√[f(θ)2+f'(θ)2] dθ

    3. The attempt at a solution

    Given f(θ)2 is equal to cos2θ+2cosθ+1

    and f'(θ)2=sin2θ

    I arrive at the integral ∫αβ√[2cosθ+2] dθ which I cannot for the life of me solve for. It's been a while since my calc II class so I flipped through my textbook to see if I could find a solution. I cannot do u substitution as far as I can tell nor integration by parts and I couldn't find anything similar to the form above in the table of integrals.
  2. jcsd
  3. Feb 3, 2012 #2


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