is, of course, the circle with center at the origin and radius a. The line x+ y= a goes through (a, 0) and (0, a). This problem is ambiguous as there are two regions bounded by those. I am going to assume they the smaller region, to the upper right of the line.
For that region, x obviously varies from 0 to a and, for each a, y varies from y= a- x to . Your integrals should be set up as
Do you have to formulas for finding the centroid (in section 15.5)? You should be able to use "symmetry" to cut your work in half.