Polar Arc Length

dtl42 · Mar 25, 2008

1. The problem statement, all variables and given/known data
Find the length of the spiral of r=1/theta for theta[tex]\geq[/tex]2 [tex]\pi[/tex]

2. Relevant 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

dynamicsolo · Mar 26, 2008

dtl42 said: ↑

[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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Polar Arc Length

dtl42

dynamicsolo

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