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Definite Integral Length of vector r(t)

  1. Feb 11, 2009 #1
    1. The problem statement, all variables and given/known data
    Evaluate the integral length of r(t)=[tihat +t^2jhat]dt from 0 to 2

    2. Relevant equations

    3. The attempt at a solution
    I think I should find the length of r(t) first which would be sqrt(t^2ihat+t^4jhat). However I'm not sure how I would integrate sqrt(t^2ihat+t^4jhat).
  2. jcsd
  3. Feb 11, 2009 #2


    Staff: Mentor

    You can also write r(t) as (x(t), y(t)), where it's understood that this is a vector in R^2. Here x(t) = t and y(t) = t^2. For arc length between t = 0 and t = 2, your integral should be:
    [tex]\int_0^2 \sqrt{(dx/dt)^2 + (dy/dt)^2} dt[/tex]
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