Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1016

\[\boxed{\mathbf{1016}\mathbf{.}}\]

\[1)\ y = x^{2} + 3x\]

\[Пересечения\ с\ осью\ x:\]

\[x^{2} + 3x = 0\]

\[(x + 3) \bullet x = 0\]

\[x_{1} = - 3\ и\ x_{2} = 0.\]

\[S = \int_{- 3}^{0}{\left( x^{2} + 3x \right)\text{\ dx}} =\]

\[= \left. \ \left( \frac{x^{3}}{3} + 3 \bullet \frac{x^{2}}{2} \right) \right|_{- 3}^{0};\]

\[Ответ:\ \ 4,5.\]

\[2)\ y = x^{2} - 4x + 3\]

\[Пересечения\ с\ осью\ x:\]

\[x^{2} - 4x + 3 = 0\]

\[D = 4^{2} - 4 \bullet 3 = 16 - 12 = 4\]

\[x_{1} = \frac{4 - 2}{2} = 1;\text{\ \ }x_{2} = \frac{4 + 2}{2} = 3.\]

\[S = \int_{1}^{3}{\left( x^{2} - 4x + 3 \right)\text{\ dx}} =\]

\[= \left. \ \left( \frac{x^{3}}{3} - 4 \bullet \frac{x^{2}}{2} + 3 \bullet \frac{x^{1}}{1} \right) \right|_{1}^{3} =\]

\[= \left. \ \left( \frac{x^{3}}{3} - 2x^{2} + 3x \right) \right|_{1}^{3};\]

\[= - 1 - \frac{1}{3} = - 1\frac{1}{3}.\]

\[Ответ:\ \ 1\frac{1}{3}.\]