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JEE Main 2026 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 5 April 2026, Shift 1, Maths Q20

Question 20 of 75 in this shift, Maths question 20 of 25, Section A.

The value of the integral

\int_{\pi/6}^{\pi/3}\left(\frac{4 - \operatorname{cosec}^2 x}{\cos^4 x}\right)dx

is:

(1) $\frac{11}{\sqrt{3}}$
(2) $\frac{16}{\sqrt{3}}$
(3) $\frac{32}{3\sqrt{3}}$ Official answer
(4) $\frac{64}{3\sqrt{3}}$

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Even Power of Secant Substitution

Same idea in other shifts

Asked 2× in all

9 Jan 2020, Shift 2 · Q62If $\int\frac{d\theta}{\cos^2\theta(\tan2\theta+\sec2\theta)}=\lambda\tan\theta+2\log_e|f(\theta)|+C$ where $C$ is a constant of…MediumSingle 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.