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May 4th, 2016, 06:17 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 09:45 PM. 
May 4th, 2016, 06:25 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,559 Thanks: 2558 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, 06:25 PM  #3 
Member Joined: May 2015 From: Earth Posts: 64 Thanks: 0 
Thanks for the quick answer archie!

May 4th, 2016, 06:26 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,559 Thanks: 2558 Math Focus: Mainly analysis and algebra 
It's a circle of radius 2, not 4.


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finding, graph, length, polar 
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