Question

Вычислить $\int\limits^3_1 {(x-2)^{2}} \, dx$

Answer 1

$\large \\ \int_{1}^{3}(x-2)^2\mathrm{dx}=\int_{1}^{3}(x-2)^2\mathrm{d(x-2)}={(x-2)^3\over3}|_{1}^{3}={(3-2)^3\over3}-{(1-2)^3\over3}={1\over3}-{(-1)\over3}={2\over3}$