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Math Help - arc length

  1. #1
    Junior Member
    Joined
    Sep 2008
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    54

    arc length

    how to compute the arclength function s(t) with the curve r=(e^t cos(-3t),e^t sin(-3t),e^t)....i got stuck when i was doing the derivative parts.

    And also how to find the length of curve if i given two points with r(t), for example, if i have r(t)=(10t,5t^2,5 Int) and i have to find the length of curve with points, (10,5,0) and (50,125, 5 In(5)) <br />

    Help =( Plz help..
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  2. #2
    Member
    Joined
    May 2008
    Posts
    106
    for the second part you should notice the points given are when t=1 and t=5 therefore it would be

    s=\int_{1}^{5}\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{d  t})^2+(\frac{dz}{dt})^2}dt

    NB with latex you write the natural log as \ln to get \ln
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