Calculating Arc Length for Polar Curve r = theta^(2)

[stau40]

Homework Statement

Find the length of r = theta^(2) for 0<=theta<=pi

Homework Equations

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

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!

 

[rock.freak667]

You could rewrite it as

[tex] \sqrt{\theta^4 +4\theta^2} = \theta \sqrt{\theta^2 +4}[/tex]

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

 

[stau40]

Got it, thanks!