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 Calculus Calculus Math Forum

 May 4th, 2016, 05:17 PM #1 Member   Joined: May 2015 From: Earth Posts: 64 Thanks: 0 Finding the length of a graph (polar) Given that $r=-4\sin(\theta)$, how does one find the length of the curve for this graph? I took the integral of $\displaystyle \sqrt{16\sin(\theta)^2 + 16\cos(\theta)^2}$ from 0 to 2$\pi$, which would give me 8$\pi$ as my answer. However, the correct answer is 4$\pi$. Why is this? Is the integral from 0 to $\pi$ instead? Does this mean if I were to find the area of this shape the integral would also be to $\pi$ instead of 2$\pi$? Thanks. Last edited by skipjack; May 4th, 2016 at 08:45 PM. May 4th, 2016, 05:25 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,615 Thanks: 2604 Math Focus: Mainly analysis and algebra Yes. The domain is between zero and $\pi$. After that, it just starts tracing out the same shape again. Yes, for the area, you would also be integrating from zero to $\pi$. May 4th, 2016, 05:25 PM #3 Member   Joined: May 2015 From: Earth Posts: 64 Thanks: 0 Thanks for the quick answer archie! May 4th, 2016, 05:26 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,615 Thanks: 2604 Math Focus: Mainly analysis and algebra It's a circle of radius 2, not 4. Tags finding, graph, length, polar Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Jas17 Computer Science 1 November 8th, 2015 07:38 PM fredlo2010 Calculus 0 November 2nd, 2014 05:12 PM 1love Calculus 3 May 23rd, 2012 09:27 PM IneedofHelp Algebra 0 November 16th, 2011 08:19 PM alex5 Calculus 6 May 17th, 2009 02:45 PM

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