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Math Help - Arc length parametrization of 1/3 t^3 i + 1/2 t^2 j ?

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    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  r(t) = \frac {u^3}{3}i + \frac{u^2}{2}j ?
    t>= 0, t=0 is the reference point.

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

    Thanks in advance!
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    Quote Originally Posted by Korgoth28 View Post
    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  r(t) = \frac {u^3}{3}i + \frac{u^2}{2}j ?
    t>= 0, t=0 is the reference point.

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

    Thanks in advance!
    more like calc I ...

    \sqrt{t^4 + t^2} = \sqrt{t^2(t^2+1)} = t\sqrt{t^2+1}

    substitution ... u = t^2+1
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    Well I feel dumb. Thank you very much!
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