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Friday, 9 October

JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 11 April 2023, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

The 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 to
  1. (1)log⁡e((2+5)21+5)+52\log_e\left(\frac{(2+\sqrt{5})^2}{\sqrt{1+\sqrt{5}}}\right) + \frac{\sqrt{5}}{2}
  2. (2)log⁡e(2(2+5)21+5)−52\log_e\left(\frac{\sqrt{2}(2+\sqrt{5})^2}{\sqrt{1+\sqrt{5}}}\right) - \frac{\sqrt{5}}{2}Official answer
  3. (3)log⁡e(2(2+5)1+5)−52\log_e\left(\frac{2(2+\sqrt{5})}{\sqrt{1+\sqrt{5}}}\right) - \frac{\sqrt{5}}{2}
  4. (4)log⁡e(2(3−5)21+5)+52\log_e\left(\frac{\sqrt{2}(3-\sqrt{5})^2}{\sqrt{1+\sqrt{5}}}\right) + \frac{\sqrt{5}}{2}

Official answer

Option 2

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. 9 Apr 2024, Shift 2 · Q12The value of the integral ∫−12log⁡e(x+x2+1)dx\int_{-1}^{2}\log_e\left(x+\sqrt{x^2+1}\right)dx isMediumSingle 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.