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Friday, 9 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 9 April 2024, Shift 2, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

The value of the integral ∫−12log⁡e(x+x2+1)dx\int_{-1}^{2}\log_e\left(x+\sqrt{x^2+1}\right)dx is
  1. (1)2−5+log⁡e(9+451+2)\sqrt{2}-\sqrt{5}+\log_e\left(\frac{9+4\sqrt{5}}{1+\sqrt{2}}\right)Official answer
  2. (2)5−2+log⁡e(9+451+2)\sqrt{5}-\sqrt{2}+\log_e\left(\frac{9+4\sqrt{5}}{1+\sqrt{2}}\right)
  3. (3)2−5+log⁡e(7+451+2)\sqrt{2}-\sqrt{5}+\log_e\left(\frac{7+4\sqrt{5}}{1+\sqrt{2}}\right)
  4. (4)5−2+log⁡e(7+451+2)\sqrt{5}-\sqrt{2}+\log_e\left(\frac{7+4\sqrt{5}}{1+\sqrt{2}}\right)

Official answer

Option 1

NTA final key.

Chapter
Integrals
Topic
Integration by Parts
Idea tested
Logarithm of Quadratic Roots

Same idea in other shifts

Asked 2× in all
  1. 11 Apr 2023, Shift 1 · Q15The value of the integral ∫−log⁡e2log⁡e2ex(log⁡e(ex+1+e2x))dx\int_{-\log_e 2}^{\log_e 2} e^x\left(\log_e\left(e^x + \sqrt{1+e^{2x}}\right)\right)dx is equal toHardSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.