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Homework Help: Arc length

  1. Sep 26, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the length of the path traced out by a particle moving on a curve according to the given equation during the time interval specified in each case.

    The equation is r(t) = a(cos t + t sin t)i + a(sin t - t Cos t)j, 0</=t</=2pi, a>0

    2. Relevant equations

    Arc length = interval (r'(t)dt)

    3. The attempt at a solution

    I found the derviative of r(t) to be r'(t) = cost + tsint +atcost +sintt -tcost +atsint
    Integrating this from 0->2pi I keep getting 0 because it is subtracting itself. The answer is supposed to be 2pi2a. What am I doing wrong?
  2. jcsd
  3. Sep 26, 2014 #2


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    ##\vec{r}(t)## is a vector as is its derivative. You can't simply erase the ##\hat{i}## and ##\hat{j}##.
  4. Sep 26, 2014 #3


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    And the formula for arc length (integral, not interval) is incorrect. The integrand is ##|\vec r'(t)|##.
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