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Homework Help: Work with a line integral

  1. May 6, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the work doneby the force field F on a particle that moves along the curve C.
    F(x,y)=xy i + x^2j
    C: x=y^2 from (0,0) to (1,1)

    2. Relevant equations

    [tex]\int[/tex]F dot dr=[tex]\int^{b}_{a}F(r(t))dotr'(t)dt[/tex]

    3. The attempt at a solution

    Okay, so I parametrized x=t and y=t^2 (giving r(t)=ti+t^2j right?) and substituted those values in for x and y in F, dotted that with 1i+2tj because I think that it is the derivative of r, if the parametric equations for r are x=t and y=t^2. I then took the integral of the dot product i just took over the interval 0 to 1. I ended up with 3/4 but the correct answer is 3/5
  2. jcsd
  3. May 6, 2009 #2


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    Homework Helper

    No, the curve is x=y^2 not y=x^2 so your parametric form of y should be [tex]y=\sqrt{t}[/tex]. Alternatively use: [tex]y=t[/tex] and [tex]x=t^2[/tex].
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