JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 24 June 2022, Shift 2, Maths Q6

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

The value of the integral

\int_{-\pi/2}^{\pi/2} \frac{dx}{(1+e^x)(\sin^6 x + \cos^6 x)}

is equal to

(1) $2\pi$
(2) $0$
(3) $\pi$ 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
2 Apr 2025, Shift 2 · Q19Let $(a, b)$ be the point of intersection of the curve $x^2 = 2y$ and the straight line $y - 2x - 6 = 0$ in the second quadrant. Then the…MediumSingle correct
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
25 Jun 2022, Shift 1 · Q2The 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 :MediumSingle 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.