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## Homework Statement

Let D be the region given as the set of (x,y) where 1 <! x^2+y^2 <! 2 and y !<0. Is D an elementary region? Evaluate [tex]\int\int_{D} f(x,y) dA[/tex] where f(x,y) = 1+xy.

## Homework Equations

## The Attempt at a Solution

So I understand that this is two concentric circles(an elementary region) which I can break down into two halves. So what I attempted was to break it into two times the first integral

of x from 2^(1/2) to 0 and the y from (1-x^2)^(1/2) to (2-x^2)^(1/2) so for my final solution I got (pi + 2)/4 the correct solution was pi/2 so I looked up the solution and they used the limit of x from 1 to 2^(1/2). That didn't make a whole lot of sense to me because x actually goes from 0 to 2^(1/2) doesn't it? Can someone attempt to explain why they chose their limits of integration the way they did? Is my method correct and maybe I just screwed up during the stupid Trig. Substitutions which is also very likely. Thanks~