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Math Help - Arc Length

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    Arc Length

    Consider the path r(t) = (10t, 5t^2, 5lnt) defined for t > 0.
    Find the length of the curve between the points (10, 5, 0) and (20, 20, 5 ln(2)).


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    Last edited by jffyx; March 9th 2009 at 10:12 PM. Reason: ln not log. Sorry
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    Quote Originally Posted by jffyx View Post
    Consider the path r(t) = (10t, 5t^2, 5lnt) defined for t > 0.
    Find the length of the curve between the points (10, 5, 0) and (20, 20, 5 ln(2)).


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    L = \int_{t=1}^{t=2} \sqrt{100 + 100t^2 + \frac{25}{t^2}} \, dt = \int_{t=1}^{t=2} \frac{1}{t} \sqrt{(10t^2 + 5)^2} \, dt = \, ....
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    How did you determine the interval of integration?
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    the path r(t) = (10t, 5t^2, 5lnt) defined for t > 0.
    Find the length of the curve between the points (10, 5, 0) and (20, 20, 5 ln(2)).
    What value of t makes (10t, 5t^2, 5ln t) equal to (10, 5, 0)? What value of t makes (10t, 5t^2, 5 ln t) equal to (20, 20, 5 ln 2)?
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