JEE Main 2022 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 27 July 2022, Shift 1, Maths Q8

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

Let

I = \int_{\pi/4}^{\pi/3} \left(\dfrac{8\sin x - \sin 2x}{x}\right) dx

. Then

(1) $\dfrac{\pi}{2} < I < \dfrac{3\pi}{4}$
(2) $\dfrac{\pi}{5} < I < \dfrac{5\pi}{12}$
(3) $\dfrac{5\pi}{12} < I < \dfrac{\sqrt{2}}{3}\pi$ Official answer
(4) $\dfrac{3\pi}{4} < I < \pi$

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Bounding and Estimation Property

Same idea in other shifts

Asked 4× in all

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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.