Arc length of the spiral r = 1/θ for θ ≥ 2π

[dtl42]

Homework Statement

Find the length of the spiral of r=1/theta for theta$$\geq$$2 $$\pi$$

Homework Equations

$$\int$$$$\sqrt{r^{2}+r'^{2}}$$

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 $$\pi$$ to infinity, but could not come up with a definitive answer. I think it might be infinity, but cannot show it legitimately

 

[dynamicsolo]

$$\int$$$$\sqrt{r^{2}+r'^{2}} d\theta$$

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 .)