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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 June 2022, Shift 2, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

If ∫1x1−x1+x dx=g(x)+c\int \frac{1}{x}\sqrt{\frac{1 - x}{1 + x}}\, dx = g(x) + c, g(1)=0g(1) = 0, then g(12)g\left(\frac{1}{2}\right) is equal to :
  1. (1)log⁡e(3−13+1)+π3\log_e\left(\frac{\sqrt{3} - 1}{\sqrt{3} + 1}\right) + \frac{\pi}{3}Official answer
  2. (2)log⁡e(3+13−1)+π3\log_e\left(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\right) + \frac{\pi}{3}
  3. (3)log⁡e(3+13−1)−π3\log_e\left(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\right) - \frac{\pi}{3}
  4. (4)12log⁡e(3−13+1)−π6\frac{1}{2}\log_e\left(\frac{\sqrt{3} - 1}{\sqrt{3} + 1}\right) - \frac{\pi}{6}

Official answer

Option 1

NTA final key.

Chapter
Integrals
Topic
Integration by Substitution
Idea tested
Cosine Double Angle Radical Substitution

Same topic in other shifts

All Integration by Substitution questions
  1. 5 Apr 2026, Shift 1 · Q20The value of the integral ∫π/6π/3(4−cosec⁡2xcos⁡4x)dx\int_{\pi/6}^{\pi/3}\left(\frac{4 - \operatorname{cosec}^2 x}{\cos^4 x}\right)dx is:MediumSingle correct
  2. 5 Apr 2026, Shift 2 · Q18Let (21−a+21+a)(2^{1-a}+2^{1+a}), f(a)f(a), (3a+3−a)(3^a+3^{-a}) be in A.P. and α\alpha be the minimum value of f(a)f(a). Then the value of the integral…HardSingle correct
  3. 3 Apr 2025, Shift 1 · Q18Let f(x)=∫x33−x2 dxf(x) = \int x^3\sqrt{3 - x^2}\,dx. If 5f(2)=−45f(\sqrt{2}) = -4, then f(1)f(1) is equal toMediumSingle correct
  4. 4 Apr 2025, Shift 2 · Q25If…HardNumerical value
  5. 7 Apr 2025, Shift 2 · Q24If…HardNumerical value
  6. 5 Apr 2024, Shift 1 · Q11The integral ∫0π/4136sin⁡x3sin⁡x+5cos⁡x dx\int_0^{\pi/4}\frac{136\sin x}{3\sin x+5\cos x}\,dx is equal to :MediumSingle 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.