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 aretworegions 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

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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.