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Find the length of the curve from 0 to 1

  1. Sep 13, 2013 #1
    1. The problem statement, all variables and given/known data

    find the length of the curve… r(t) = <4t, t^(2) + 1/6(t)^(3)> from 0≤t≤1

    2. Relevant equations

    L(t) = ∫a to b √(dx/dt)^(2) +(dy/dt)^(2) + (dz/dt)^(2))dt

    3. The attempt at a solution

    After taking the derivative of all components of the curve and finding the magnitude…
    ∫ 0 to 1 √(16+4t^(2) + 1/324(t)^(4))dt

    And I can't manage to simplify any further.
    I tried, doing ∫ 0 to 1 √(t)^(4) + 1296t^(2) + 5184

    I don't know how to go any further in simplifying and pulling some t's out of the radical.
    I know, it's some algebra, but I have no idea how to go about this from here.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 13, 2013 #2


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    The seem to be a few errors in the (dy/dt)2 term.
    OTOH, corecting them makes the integrand look even worse.
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