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JEE Main 2020 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 4 September 2020, Shift 2, Maths Q61

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

The integral

\int_{\pi/6}^{\pi/3} \tan^3 x \cdot \sin^2 3x \,(2\sec^2 x \cdot \sin^2 3x + 3\tan x \cdot \sin 6x)\,dx

is equal to :

(1) $\frac{7}{18}$
(2) $-\frac{1}{9}$
(3) $\frac{9}{2}$
(4) $-\frac{1}{18}$ Official answer

Official answer

Option 4

NTA final key (Sep 2020).

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Implicit Derivative Recognition

Same idea in other shifts

Asked 2× in all

8 Apr 2023, Shift 1 · Q11Let $I(x)=\int\frac{(x+1)}{x(1+xe^x)^2}dx$ , $x>0$ . If $\lim_{x\to\infty}I(x)=0$ , then $I(1)$ 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 108 of the 174 JEE Main shifts held from 2017 to 2026.