Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 380

\[1)\ y = x^{2} - 4x + 3\]

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

\[D = 16 - 12 = 4\]

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

\[x_{2} = \frac{4 + 2}{2} = 3.\]

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

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

\[= (9 - 18 + 9) - \left( \frac{1}{3} - 2 + 3 \right) =\]

\[= - \left( \frac{1}{3} + 1 \right) = - 1\frac{1}{3}.\]

\[Ответ:\ \ 1\frac{1}{3}.\]

\[2)\ y = \cos x;\ \left\lbrack \frac{3\pi}{4};\ \pi \right\rbrack:\]

\[|S| = \int_{\frac{3\pi}{4}}^{\pi}{\cos x\text{dx}} = \left. \ \sin x \right|_{\frac{3\pi}{4}}^{\pi} =\]

\[= \sin\pi - \sin\frac{3\pi}{4} = - \frac{\sqrt{2}}{2}.\]

\[Ответ:\ \ \frac{\sqrt{2}}{2}.\]