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May 3rd, 2014, 03:08 PM   #1
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Evaluate the integral along the cycloid

$\displaystyle \int_C (z^2+1)^2dz$
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!
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June 15th, 2014, 05:17 AM   #2
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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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