Решебник по алгебре 11 класс Никольский Параграф 6. Первообразная и интеграл Задание 80

\[\boxed{\mathbf{80}.}\]

\[\textbf{а)}\ W = \int_{a}^{b}{f(x)\text{dx}} =\]

\[= \int_{0}^{3}{(2x - 1)\text{dx}} = \left. \ x^{2} - x \right|_{0}^{3} =\]

\[= \left( 3^{2} - 3 \right) - \left( 0^{2} - 0 \right) = 6.\]

\[Ответ:W = 6.\]

\[\textbf{б)}\ W = \int_{a}^{b}{f(x)\text{dx}} =\]

\[= \int_{0}^{2}{\left( - x^{2} + 4 \right)\text{dx}} =\]

\[= \left. \ \left( - \frac{1}{3}x^{3} + 4x \right) \right|_{0}^{2} =\]

\[= - \frac{8}{3} + 8 = \frac{16}{3} = 5\frac{1}{3}.\]

\[Ответ:W = 5\frac{1}{3}.\]