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Confused with double integral

  1. Jan 31, 2006 #1
    given f(x,y) = x-y

    R is a triangle with vertices (2,9), (2,1), (-2,1)
    then i need to find I,

    I = int. int. (x-y) dx dy

    i was taught to use this range when i do the dbl. integration
    1 <= y <= 9

    (y-5)/2 <= x <= 2

    i want to ask, why can't i use this range:

    1 <= y <= 9

    -2 <= x <= (y-5)/2

    thank you.
  2. jcsd
  3. Jan 31, 2006 #2


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    Try making a graphic, you'll see that with your ranges, you're covering the 'other triangle' when you complete the rectangle (by adding the point (-2,9))
    Last edited: Jan 31, 2006
  4. Jan 31, 2006 #3
    Oh, thank you, TD!!
  5. Jan 31, 2006 #4


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    You're welcome! It's always handy to make a fast sketch of the problem, it makes it a lot easier to determine the ranges if you 'see' the area rather than trying to do it with the equations only.
  6. Jan 31, 2006 #5
    i got confused again.

    do you mean (-2,9)??
  7. Jan 31, 2006 #6


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    Yes of course, for that rectangle I mentioned :smile:

    I'll correct, thanks.
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