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Homework Help: Double Integral

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data
    Evaluate the following definite two-dimensional integrals over the specified domains of integration.

    f(x,y)=min(x,y), over the region {(x,y) : 0 [tex]\leq[/tex] x [tex]\leq[/tex] 2, 0 [tex]\leq[/tex] y [tex]\leq[/tex] 1}


    2. Relevant equations



    3. The attempt at a solution
    I'm not even sure where to start because I'm not sure what the problem even means by f(x,y)=min(x,y). HELP!
     
  2. jcsd
  3. Jan 21, 2010 #2

    dx

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    min(x,y) means minimum of x and y. For example, in the region x < y, f(x,y) = x.
     
  4. Jan 21, 2010 #3
    So if I integrate first from 0 [tex]\leq[/tex] y [tex]\leq[/tex] 1 then the x bounds, my f(x,y)=y? I'm a little confused over this. I don't remember going over this in calculus and this homework is supposed to be a calculus review.
     
  5. Jan 21, 2010 #4

    dx

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    Divide the region {(x,y) : 0 < x < 2, 0 < y < 1} into two parts, one where f(x,y) = x, and one where f(x,y) = y. Then do the usual double integration for the two regions seperately.
     
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