If the value of the integral ${\int }_{0}^{1/2}\frac{{x}^{2}}{{\left(1-{x}^{2}\right)}^{3/2}}dx$ is $\frac{k}{6}$, then $k$ is equal to [JEE Main 2020, 3 Sep (Shift 2)]

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If the value of the integral \({\int }_{0}^{1/2}\frac{{x}^{2}}{{\left(1-{x}^{2}\right)}^{3/2}}dx\) is \(\frac{k}{6}\), t…

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