Boundaries for double integrals?

[sherrellbc]

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.
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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.

 

[CompuChip]

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).