That would be correct if the base in the xy-plane were the disk with center at (0, 0) with radius (you have but you mean ). But in fact, it is the intersection of the two disks, , the circle with center at (0, 0) and radius 1, and . The points of intersection are and which correspond to , r= 1 and , r= 1 in polar coordinates.
You will need to do this as three separate integrals. The main one will be with going from to , r from 0 to 1. That leaves the two small sections between the straight lines from (0, 0) to and from (0, 0) to and the circle . Taking from to , r goes from 1 to the curve which, in polar coordinates is or for r not 0, so that r goes from 0 to . For the last piece, goes from to and, for each r goes from 0 to also.