# Thread: Arc length parametrization of 1/3 t^3 i + 1/2 t^2 j ?

1. ## Arc length parametrization of 1/3 t^3 i + 1/2 t^2 j ?

Hello! I'm new to this forum so bear with me as I figure latex out. I have a calc 3 test on Wednesday so be expecting a lot of questions from me :-)

My question is how do I find the arc length parametrization with the same orientation for $\displaystyle r(t) = \frac {u^3}{3}i + \frac{u^2}{2}j$?
t>= 0, t=0 is the reference point.

I got to $\displaystyle \int{\sqrt{t^4 + t^2}}$ but can't figure out how to integrate. Is there some calc 2 trick I'm forgetting?

2. Originally Posted by Korgoth28
Hello! I'm new to this forum so bear with me as I figure latex out. I have a calc 3 test on Wednesday so be expecting a lot of questions from me :-)

My question is how do I find the arc length parametrization with the same orientation for $\displaystyle r(t) = \frac {u^3}{3}i + \frac{u^2}{2}j$?
t>= 0, t=0 is the reference point.

I got to $\displaystyle \int{\sqrt{t^4 + t^2}}$ but can't figure out how to integrate. Is there some calc 2 trick I'm forgetting?

$\displaystyle \sqrt{t^4 + t^2} = \sqrt{t^2(t^2+1)} = t\sqrt{t^2+1}$
substitution ... $\displaystyle u = t^2+1$