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Polar Arc Length

  • Thread starter dtl42
  • Start date
  • #1
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1. Homework Statement
Find the length of the spiral of r=1/theta for theta[tex]\geq[/tex]2 [tex]\pi[/tex]


2. Homework Equations
[tex]\int[/tex][tex]\sqrt{r^{2}+r'^{2}}[/tex]


3. The Attempt at a Solution
I thought of the formula for polar arc length, which is the integral of the square root of the sum of the square of r and the square of r'. I tried to evaluate this from 2 [tex]\pi[/tex] to infinity, but could not come up with a definitive answer. I think it might be infinity, but cannot show it legitimately
 

Answers and Replies

  • #2
dynamicsolo
Homework Helper
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[tex]\int[/tex][tex]\sqrt{r^{2}+r'^{2}} d\theta[/tex]
You probably aren't getting help because you haven't shown any work. What did you set up as your integrand? Your limits for the improper integral are correct; it really is possible that the integral doesn't converge. (This curve is called a hyperbolic spiral -- see http://mathworld.wolfram.com/HyperbolicSpiral.html .)
 

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