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Homework Help: Parametric curve

  1. Apr 6, 2005 #1
    Consider the parametric curve given by the equations
    [tex]x(t) = t^2+30t-11[/tex]
    [tex]y(t)=t^2+30t+38[/tex]
    How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=9 ?

    well since the bounds are already given (0->9), i just need help on setting up the integral. here's what i done:

    [tex]dx/dt = 2t+30[/tex]

    my integral:

    [tex]\int_{0}^{9}(t^2+30t+38)*(2t+30)[/tex]

    but i get the incorrect answer when i integral it, can someone help me set it up?
     
  2. jcsd
  3. Apr 6, 2005 #2

    ehild

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    Homework Helper

    The distance travelled is

    [tex]\int_{0}^{9}\sqrt{(dx/dt)^2+(dy/dt)^2}dt[/tex]

    You either do this integral, or notice that the curve is a straight line.

    ehild
     
  4. Apr 6, 2005 #3
    What is the formula for calculating curve's length? You have calculated the area under the curve, not the length.
     
  5. Apr 6, 2005 #4
    thank you, i got it correct
     
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