# Polar Arc Length

1. Mar 25, 2008

### dtl42

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

2. Relevant equations
$$\int$$$$\sqrt{r^{2}+r'^{2}}$$

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

2. Mar 26, 2008

### dynamicsolo

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 .)