Question

вычислите интеграл !

Answer 1

$\int\limits^1_0{\sqrt[7]{x^{3}}}\,dx\\\int\limits{\sqrt[7]{x^{3}}}\,dx\\\int\limits{x^{\frac{3}{7}}}\,dx\\\frac{7\times\sqrt[7]{x^{3}}}{10}\\\left.\begin{matrix}\frac{7\times\sqrt[7]{x^{3}}}{10}\end{matrix}\right|^1_0\\\frac{7\times1\sqrt[7]{x^{3}}}{10}-\frac{7\times0\sqrt[7]{x^{3}}}{10}\\\frac{7}{10}\\0.7$

Answer 2

$\binom{1}{0} \int \sqrt[7]{ {x}^{3} } dx = \\ = \binom{1}{0} \int {x}^{ \frac{3}{7} } dx = \\ = \frac{ {x}^{ \frac{3}{7} + 1} }{ \frac{3}{7} + 1 } \binom{1}{0} = \\ = \frac{7}{10} {x}^{ \frac{10}{7} } \binom{1}{0} = \\ =0.7\times {1}^{ \frac{10}{7} }- 0\times{0}^{ \frac{10}{7} } = 0.7$