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Homework Help: Line Integral - Vector Calculus

  1. Mar 31, 2012 #1
    1. The problem statement, all variables and given/known data
    Calculate the line integral:
    f(x,y) = (x² - 2xy)î + (y² - 2xy)j, between the points (-1,1) and (1,1) along the parabola y = x².
    (resp: -14/15)

    The attempt at a solution
    I thought something like this: substitue y = x², and then integrate de f(x,y). And then evaluate from -1 to 1, but it didn't work, obviously. How should I start solving this? I think I didn't get the concept about this kind of exercise...
  2. jcsd
  3. Mar 31, 2012 #2


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    Science Advisor

    If it didn't work then you must have made an error in the integrall. What, exactly, did you do?

    The integral of this will be [itex]\int (x^2 - 2xy)dx+ (y^2- 2xy)dy[//itex]. Did you remember to put dy in terms of x also?
  4. Mar 31, 2012 #3
    Ahh, that's exactly what I was forgetting! Thank you!!
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