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Math Help - Find length of the curve help

  1. #1
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    Find length of the curve help

    find the length of the curve r(t) = <2t, t^2, 1/3t^3>

    I did this
    r'(t) = <2, 2t, t^2>

    |r'(t)|

    When I take the integral, I don't know how to solve for it.
    Thanks in advanced.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by khuezy View Post
    find the length of the curve r(t) = <2t, t^2, 1/3t^3>

    I did this
    r'(t) = <2, 2t, t^2>

    |r'(t)|

    When I take the integral, I don't know how to solve for it.
    Thanks in advanced.
    First, what are the boundaries on t?

    Second, the integral is \int_{t_0}^{t_f}\sqrt{\left(\frac{\,dx}{\,dt}\righ  t)^2+\left(\frac{\,dy}{\,dt}\right)^2+\left(\frac{  \,dz}{\,dt}\right)^2}\,dt=\int_{t_0}^{t_f}\sqrt{4+  4t^2+t^4}\,dt=\int_{t_0}^{t_f}\sqrt{(t^2+2)^2}\,dt =\int_{t_0}^{t_f}\left(t^2+2\right)\,dt, for t_0\leq t\leq t_f

    This is not much of a hassle to integrate.

    Does this make sense?

    --Chris
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