Calculating Polar Arc Length for r=1/theta from 2 Pi to Infinity | Homework Help

[dtl42]

Homework Statement

Find the length of the spiral of r=1/theta for theta[tex]\geq[/tex]2 [tex]\pi[/tex]

Homework Equations

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

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]

[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 .)