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May 4th, 2016, 05:17 PM   #1
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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.
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May 4th, 2016, 05:25 PM   #2
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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 $\pi$.
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May 4th, 2016, 05:25 PM   #3
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Thanks for the quick answer archie!
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May 4th, 2016, 05:26 PM   #4
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It's a circle of radius 2, not 4.
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