If the value of the integral $\int_\limits 0^{1 / 2} \frac{x^2}{\left(1-x^2\right)^{3 / 2}} d x$ is $\frac{k}{6}$, then $k$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

If the value of the integral

\int\limits_{0}^{1 / 2} \frac{x^2}{\left(1-x^2\right)^{3 / 2}} d x

\frac{k}{6}

, then

k

is equal to

View answer and explanation

Correct option: B

2 \sqrt{3}-\pi

Option B is correct. The integral is solved using trigonometric substitution, resulting in k = 2

\sqrt{3}

\pi

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