ГДЗ по алгебре и начала математического анализа 11 класс Колягин Задание 368

\[1)\ \int_{1}^{e}{\frac{1}{x}\text{\ dx}} = \left. \ \ln|x| \right|_{1}^{e} =\]

\[= \ln e - \ln 1 = 1 - 0 = 1;\]

\[2)\ \int_{0}^{\ln 2}{e^{x}\text{\ dx}} = \left. \ e^{x} \right|_{0}^{\ln 2} =\]

\[= e^{\ln 2} - e^{0} = 2 - 1 = 1;\]

\[3)\ \int_{- 2\pi}^{\pi}{\sin x\text{dx}} = \left. \ - \cos x \right|_{- 2\pi}^{\pi} =\]

\[= - \cos\pi + \cos( - 2\pi) = 2;\]

\[4)\ \int_{- 3\pi}^{0}{\cos{3x}\text{dx}} = \left. \ \frac{1}{3}\sin{3x} \right|_{- 3\pi}^{0} =\]

\[= \frac{1}{3}\sin 0 - \frac{1}{3}\sin( - 9\pi) = 0.\]