omg ok. I managed to solve them using the mathlet that plots 3D graphs. The volumes cancel out nicely for: $\int\limits_{}^{}\int\limits_{}^{} x ^{2}y\ dA$ $\int\limits_{}^{}\int\limits_{}^{} xy\ dA$ Then for $\int\limits_{}^{}\int\limits_{}^{} x ^{2 } +y\ dA$ I realized I could take out y from the integrals which reduces to $\int\limits_{}^{}\int\limits_{}^{} x ^{2}\ dA$ + $\int\limits_{}^{}\int\limits_{}^{}y\ dA$ the second integral being zero. If anyone has a smarter way to solve without using the mathlet please let me know.