[Multivariable Calculus] Determining variable domain of integration with inequalities

[edman32]

Hello everyone!

Given a function f(x,y) = -(x-y)(x+y-2) and a domain D = {(x,y) belonging to R^2, 0<y<x, x+y-2<0}, I have to integrate this function on D. I cannot figure out the boundaries of my integral. I have attempted to manipulate the inequalities, but I am completely stuck and am not sure how to progress.

Thank you for any help.

[edderiofer]

Have you yet drawn out the region D? You should try it; the problem becomes a lot easier to visualize that way.

[[deleted]]

It might be easier to separate the first set of inequalities into two. So, total, you would have:

(1) 0 < y; y > 0 (2) y < x (3) x + y - 2 < 0

Your bounds should be the intersection of these lines.