JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 August 2021, Shift 1, Maths Q69

Question 69 of 90 in this shift, Maths question 9 of 30, Section A.

The value of

\int_{-1/\sqrt{2}}^{1/\sqrt{2}} \left(\left(\frac{x+1}{x-1}\right)^2 + \left(\frac{x-1}{x+1}\right)^2 - 2\right)^{1/2} dx

is :

(1) $4\log_e(3+2\sqrt{2})$
(2) $\log_e 4$
(3) $\log_e 16$ Official answer
(4) $2\log_e 16$

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Modulus Function Interval Splitting

Same idea in other shifts

Asked 6× in all

8 Apr 2025, Shift 2 · Q19The integral $\int_{-1}^{\frac{3}{2}} \left(\left|\pi^2 x \sin(\pi x)\right|\right) dx$ is equal to :MediumSingle correct
25 Feb 2021, Shift 2 · Q86The value of $\int_{-2}^{2} |3x^2 - 3x - 6|\,dx$ is ________.MediumNumerical value
26 Feb 2021, Shift 1 · Q88The value of the integral $\int_0^{\pi}|\sin 2x|\,dx$ is _________.EasyNumerical value
2 Sep 2020, Shift 1 · Q73The integral $\int_{0}^{2}\left||x-1|-x\right|dx$ is equal to ___________.EasyNumerical value
3 Sep 2020, Shift 1 · Q60 $\int_{-\pi}^{\pi}|\pi-|x||dx$ is equal to :EasySingle correct

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.