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Use the defiinition of a line integral to evaluate

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data
    Use the definition to find the line integral of F(x,y) = (y,x) along each of the following paths.

    The parabola y = x^2 from (-1,1) to (1,1)



    2. Relevant equations

    F(x) = gradientf(x)

    ∫F(x) dx = f(b) - f(a)

    3. The attempt at a solution

    I tried (y,x) dot (t,t^2) which gave me yt+xt^2 which 2t^3 thus ∫ from 1 to -1 of 2t^3 unfortunatley this was incorrect so I just did this r(t) = (1-t)<-1,1> + t<1,1> which give
    <-1,1+2t> then ∫x^2 ds = ∫(-1)^2sqrt(4) = ∫2 dt = 2t from 0 to 1 which gives 2 this was correct however I am not sure if this is a valid way to answer
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 4, 2011 #2

    LCKurtz

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    Gold Member

    It isn't because that second method is along a straight line, not the parabola. But check that part in the red. Aren't you supposed to dot it with the derivative of < t, t2>?
     
  4. Dec 5, 2011 #3
    I will try that sorry about the late reply
     
  5. Dec 5, 2011 #4
    Lol your right I goofed it thanks man.
     
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