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\text { area }=\int_{0}^{3}(x-2)^{2} \mathrm{dx}=\int_{0}^{3} \mathrm{x}^{2}-4 \mathrm{x}+4 \mathrm{dx}=\frac{1}{3} \mathrm{x}^{3}-2 \mathrm{x}^{2}+\left.4 \mathrm{x}\right|_{0} ^{3}=3-0=3 .