I need to find the area of the ring defined by , y=0, and x=1, with the center of the ring being x=2.

Part of the problem I am having is that while I understand the concept of what I need to do, I am getting confused between how I figure out which way the slices go (parallel to x axis, or parallel to y axis), whether I need to set up the integral with respect to x or with respect to y. For example, I have , do I plug that into the integral, or do I need to solve for x (getting and then plug that into the integral? I'm not sure how to keep that all straight.

I am getting:

which becomes

Take the integral and get:

(haven't quite got the syntax of the left bracket and intervals correct) , or

The answer I get is and the book has

I'm pretty confident my setup is incorrect, but I've tried several different setups and not gotten to the correct one. I'm not sure what else to try at this point.

I would appreciate some help with the setup and also some pointers on how to set up these problems in general.

Thanks!