Решебник по алгебре 11 класс Никольский Параграф 6. Первообразная и интеграл Задание 48

\[\boxed{\mathbf{48}.}\]

\[\textbf{а)}\ f(x) = x^{3};\]

\[F(x) = \frac{x^{4}}{4};\]

\[\int_{0}^{1}{x^{3}\text{dx}} = F(1) - F(0) =\]

\[= \frac{1^{4}}{4} - \frac{0^{4}}{4} = \frac{1}{4}.\]

\[\textbf{б)}\ f(x) = x^{3};\]

\[F(x) = \frac{x^{4}}{4};\]

\[\int_{- 1}^{1}{x^{3}\text{dx}} = F(1) - F( - 1) =\]

\[= \frac{1^{4}}{4} - \frac{( - 1)^{4}}{4} = 0.\]

\[\textbf{в)}\ f(x) = x^{3};\]

\[F(x) = \frac{x^{4}}{4};\]

\[\int_{2}^{3}{x^{3}\text{dx}} = F(3) - F(2) =\]

\[= \frac{3^{4}}{4} - \frac{2^{4}}{4} = \frac{81}{4} - \frac{16}{4} = \frac{65}{4} =\]

\[= 16,25.\]