If the value of the integral $\int\limits_0^{{1 \over 2}} {{{{x^2}} \over {{{\left( {1 - {x^2}} \right)}^{{3 \over 2}}}}}} dx$ is ${k \over 6}$, then k is equal to :

Question

If the value of the integral
$\int\limits_0^{{1 \over 2}} {{{{x^2}} \over {{{\left( {1 - {x^2}} \right)}^{{3 \over 2}}}}}} dx$

is ${k \over 6}$, then k is equal to :

$2\sqrt 3 + \pi $

$3\sqrt 2 - \pi $

$3\sqrt 2 + \pi $

$2\sqrt 3 - \pi $

Solution

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