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Double integral problem (pretty basic)

  1. Nov 2, 2011 #1
    Good day, all:

    We recently hit double/triple integrals in my multivariable calculus course and I have found that my integration abilities are, well, *beyond* rusty ... and so the problem below, which is one of the very first on my current problem set, has me stumped.

    1. The problem statement, all variables and given/known data

    [itex]\int\int_{R}\frac{x}{1+xy} dA[/itex] R = { [0,1]x[0,1] = {(x,y): 0 [itex]\leq[/itex] x [itex]\leq[/itex]1, 0 [itex]\leq[/itex] y [itex]\leq[/itex]1 }

    3. The attempt at a solution

    My first and nearly only step was to turn this into an iterated integral:

    [itex]\int^{1}_{0}\int^{1}_{0}\frac{x}{1+xy} dx dy[/itex]

    ... and this is where I begin to choke and sputter. I have started to try u-substitution on this with u = 1+xy, but didn't get anything that made sense to me; some hints I have found online seem to indicate that I should be able to perform "polynomial long division" to turn this into a sum or difference of two simpler integrals, but I guess I don't sufficiently understand polynomial long division to carry this out here.

    Any hints would be much appreciated. I am considering dropping this course, but I would like to avoid that ... I need some serious integration mojo to be directly infused into my skull asap. :bugeye:

    Regards,

    Glenn
     
  2. jcsd
  3. Nov 2, 2011 #2
    Did you try integrating with respect to y first?
     
  4. Nov 2, 2011 #3
    No. I'll check it out and see what happens. Thank you.

    EDIT: That was key, of course. Jeez. ::strikes forehead::
     
    Last edited: Nov 2, 2011
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