Решебник по алгебре 11 класс Никольский Параграф 6. Первообразная и интеграл Задание 50

\[\boxed{\mathbf{50}.}\]

\[\textbf{а)}\ \int_{0}^{\frac{\pi}{2}}{\cos x\text{dx}};\]

\[F(x) = \sin x;\]

\[\int_{0}^{\frac{\pi}{2}}{\cos x\text{dx}} = \sin\frac{\pi}{2} - \sin 0 =\]

\[= 1 - 0 = 1.\]

\[\textbf{б)}\ \int_{0}^{\pi}{\cos x\text{dx}};\]

\[F(x) = \sin x;\]

\[\int_{0}^{\pi}{\cos x\text{dx}} = \sin\pi - \sin 0 =\]

\[= 0 - 0 = 0.\]

\[\textbf{в)}\ \int_{- \frac{\pi}{2}}^{\frac{\pi}{2}}{\cos x\text{dx}};\]

\[F(x) = \sin x;\]

\[\int_{- \frac{\pi}{2}}^{\frac{\pi}{2}}{\cos x\text{dx}} =\]

\[= \sin\frac{\pi}{2} - \sin\left( - \frac{\pi}{2} \right) =\]

\[= 1 - ( - 1) = 2.\]