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Evaluate a Definite Integral to find Work

  1. Jan 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Evaluate: from x=0 to x=1 and y=0 to y=1

    ∫(y^2 + 2xy(dy/dx))dx and carry the integration out over x



    2. Relevant equations



    3. The attempt at a solution
    I know how to calculate double integrals with multiple variables but the (dy/dx) throws me off and it says to carry out the integration over x which to means that it isn't a double integral at all? Can some one explain to me how to deal with this integral? Thanks!
     
  2. jcsd
  3. Jan 13, 2013 #2

    pasmith

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    The question is somewhat unclear, but I think it is asking you to evaluate the given line integral over the line [itex]y = x[/itex] from [itex](0,0)[/itex] to [itex](1,1)[/itex]. So substitute [itex]y = x[/itex] and [itex]dy/dx = 1[/itex] in the integrand and integrate with respect to [itex]x[/itex].
     
  4. Jan 13, 2013 #3

    haruspex

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    The integrand has a rather interesting property. It can be written in the form d(f(x,y)). So the answer will be independent of path.
     
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