JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q2

Question 2 of 90 in this shift, Maths question 2 of 30, Section A.

The value of

\int_0^{\pi} \frac{e^{\cos x}\sin x}{(1+\cos^2 x)(e^{\cos x}+e^{-\cos x})}\,dx

is equal to :

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

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Symmetric Limits with Exponential Denominator Trick

Same idea in other shifts

Asked 10× in all

6 Apr 2026, Shift 1 · Q18The value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{32\cos^4 x}{1+e^{\sin x}}\right)dx$ is:MediumSingle correct
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4 Apr 2024, Shift 2 · Q10If the value of the integral $\int_{-1}^{1}\frac{\cos\alpha x}{1+3^x}dx$ is $\frac{2}{\pi}$ . Then, a value of $\alpha$ isMediumSingle correct
1 Feb 2024, Shift 1 · Q27If $\int_{-\pi/2}^{\pi/2}\frac{8\sqrt{2}\cos x\,dx}{(1+e^{\sin x})(1+\sin^4 x)}=\alpha\pi+\beta\log_e(3+2\sqrt{2})$ , where $\alpha,\beta$ …HardNumerical value
29 Jan 2024, Shift 1 · Q11If the value of the integral…HardSingle correct
24 Jun 2022, Shift 2 · Q6The value of the integral $\int_{-\pi/2}^{\pi/2} \frac{dx}{(1+e^x)(\sin^6 x + \cos^6 x)}$ is equal toMediumSingle correct
27 Jun 2022, Shift 1 · Q10The value of the integral $\int_{-2}^{2} \frac{|x^3+x|}{(e^{x|x|}+1)}\,dx$ is equal to :MediumSingle correct
26 Aug 2021, Shift 2 · Q67The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{1+\sin^2 x}{1+\pi^{\sin x}}\right)\mathrm{d}x$ is :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 108 of the 174 JEE Main shifts held from 2017 to 2026.