My Math Forum Evaluate the integral along the cycloid

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 May 3rd, 2014, 03:08 PM #1 Senior Member   Joined: Jan 2014 Posts: 196 Thanks: 3 Evaluate the integral along the cycloid Evaluate $\displaystyle \int_C (z^2+1)^2dz$ along the cycloid $\displaystyle x=a(\theta - sin\theta)$ , $\displaystyle y=a(1-cos\theta)$ from $\displaystyle \theta=0$ to $\displaystyle \theta=2\pi$ For the solution, will I be left w/ a function of $\displaystyle a$?? Thanks for any help!
 June 15th, 2014, 05:17 AM #2 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Let γ be the cycloid, since γ(0)=γ(2π)=0 and $(z^2+1)^2$ is analytic over the closed curve the line integral equals 0.

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