(adsbygoogle = window.adsbygoogle || []).push({}); 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=∫_{α}^{β}√[f(θ)^{2}+f'(θ)^{2}] dθ

3. The attempt at a solution

Given f(θ)^{2}is equal to cos^{2}θ+2cosθ+1

and f'(θ)^{2}=sin^{2}θ

I arrive at the integral ∫_{α}^{β}√[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.

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# Computing Arc Length and Cannot Solve the Integral

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