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JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 July 2022, Shift 1, Maths Q6

Question 6 of 90 in this shift, Maths question 6 of 30, Section A.

The integral

\int_0^{\pi/2} \frac{1}{3 + 2\sin x + \cos x}\, dx

is equal to :

(1) $\tan^{-1}(2)$
(2) $\tan^{-1}(2) - \frac{\pi}{4}$ Official answer
(3) $\frac{1}{2}\tan^{-1}(2) - \frac{\pi}{8}$
(4) $\frac{1}{2}$

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Weierstrass Substitution

Same idea in other shifts

Asked 2× in all

2 Apr 2017 (offline) · Q75The integral $\int_{\pi/4}^{3\pi/4}\frac{dx}{1+\cos x}$ 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.