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Boundaries for double integrals?

  1. Jul 14, 2013 #1
    And your boundaries are defined as: 0 < x < y < 1
    How do you know the relationship between x and beyond this?

    That is, we know that y is between x and 1, but x is between 0 and y. We have a loop. In a specific example, I know the answer is, where f(x,y) = 8xy

    ∫∫8xy dx dy

    With bounds 0 to y, for the inner integral, and 0 to 1 for the outer.
    As an aside, I would make this much better, in terms of aesthetics, but I always have a very hard time with formatting for some reason.
  2. jcsd
  3. Jul 15, 2013 #2


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    You let x run from 0 to 1, and for every value of x you let y run from x to 1. Then the inequality is always satisfied (if you make sure y < x then automatically x > y).

    If unsure, draw a picture by coloring the relevant area in a unit triangle (hint: draw the line y = x).
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