Решебник по алгебре 11 класс Никольский Параграф 6. Первообразная и интеграл Задание 35

\[\boxed{\mathbf{35}.}\]

\[\textbf{а)}\ y = \sin x;\lbrack - \pi;0\rbrack;\lbrack 0;\ \pi\rbrack;\]

\[\left| S_{1} \right| = \left| S_{2} \right|:\]

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

\[= - S_{1} + S_{2} = 0.\]

\[\textbf{б)}\ y = \cos x;\left\lbrack - \frac{\pi}{2};\frac{\pi}{2} \right\rbrack;\ \ \left\lbrack \frac{\pi}{2};\ \frac{3\pi}{2} \right\rbrack;\]

\[\left| S_{1} \right| = \left| S_{2} \right|:\]

\[\int_{- \frac{\pi}{2}}^{\frac{\pi}{2}}{\cos x\text{dx}} + \int_{\frac{\pi}{2}}^{\frac{3\pi}{2}}{\cos x\text{dx}} =\]

\[= S_{1} - S_{2} = 0.\]