# Polar Arc Length Question

1. Jun 21, 2010

### stau40

1. The problem statement, all variables and given/known data
Find the length of r = theta^(2) for 0<=theta<=pi

2. Relevant equations
Arc length s = antiderivative of sq rt (f (theta)^(2) + f (derivative theta)^(2))

3. The attempt at a solution
I have worked my way to the antiderivative of sq rt (theta^(4) + 4(theta)^(2)) but I'm not sure where to go from here. I've been looking for a trig identity that will help me thru the antiderivative and get rid of the sq. rt but haven't had any luck. Is there something I'm overlooking? Thanks in advance!

2. Jun 21, 2010

### rock.freak667

You could rewrite it as

$$\sqrt{\theta^4 +4\theta^2} = \theta \sqrt{\theta^2 +4}$$

and use a trig substitution or look it up in a http://en.wikipedia.org/wiki/List_of_integrals_of_irrational_functions" [Broken]

Last edited by a moderator: May 4, 2017
3. Jun 21, 2010

### stau40

Got it, thanks!