If the value of the integral $\int_0^{1/2} \frac{x^2}{(1 - x^2)^{3/2}} dx$ is $\frac{k}{6}$, then k is equal to :

JEE Main 2020 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 3 September 2020, Shift 2, Maths Q61

Question 61 of 75 in this shift, Maths question 11 of 25.

If the value of the integral

\int_0^{1/2} \frac{x^2}{(1 - x^2)^{3/2}} dx

\frac{k}{6}

, then k is equal to :

(1) $2\sqrt{3} + \pi$
(2) $2\sqrt{3} - \pi$ Official answer
(3) $3\sqrt{2} - \pi$
(4) $3\sqrt{2} + \pi$

Official answer

Option 2

NTA final key (Sep 2020).

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Trigonometric Substitution

Same idea in other shifts

Asked 3× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.