Найти определенный интеграл[tex] \int\limits^2_1 \frac{x}{ \sqrt[3]{(1-x^{2})^2 } } \, dx [/tex] . Created by DECOY656. matematika-ru

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July 2022 1 5 Report

Найти определенный интеграл[tex] \int\limits^2_1 \frac{x}{ \sqrt[3]{(1-x^{2})^2 } } \, dx [/tex]

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sedinalana

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T=1-x²⇒dt=-2xdx
$\int\limits^2_1 {x/ \sqrt[3]{(1-x^2)^2} } \, dx =-1/2 \int\limits { \sqrt[3]{t^2} } \, dt =-3/2* \sqrt[3]{t} =-3/2* \sqrt[3]{1-x^2} |2-$ $1=-3/2* \sqrt[3]{-3} +3/2* \sqrt[3]{0} =3 \sqrt[3]{3} /2$

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