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Saturday, 31 October

JEE Main · Maths · Integrals

Symmetric Limits with Exponential Denominator Trick

JEE Main asked Symmetric Limits with Exponential Denominator Trick 10 times in 10 of the 108 shifts Lumi analysed, in 2021, 2022, 2024, 2025 and 2026. It belongs to Definite Integral Properties, in Integrals (Maths). The longest wait between two years asking it was 2 years. In 2021, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
10
in 10 shifts
Years
5 of 8
First asked
2021
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.07’210.11’220’230.14’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 3 in 24 shifts · 2023: 0 in 12 shifts · 2024: 3 in 18 shifts · 2025: 1 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20251 of 8
  • 20243 of 18
  • 20230 of 12
  • 20223 of 24
  • 20212 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Definite integral using king's property
  • Definite integral with exponential denominator trick

Difficulty

Easy 0Medium 8Hard 2

1 of the 10 questions had a numerical answer.

Every question

All 10 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 6 Apr 2026, Shift 1 · Q18The value of the integral ∫−π4π4(32cos⁡4x1+esin⁡x)dx\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{32\cos^4 x}{1+e^{\sin x}}\right)dx is:MediumSingle correct
  2. 2 Apr 2025, Shift 2 · Q19Let (a,b)(a, b) be the point of intersection of the curve x2=2yx^2 = 2y and the straight line y−2x−6=0y - 2x - 6 = 0 in the second quadrant. Then the…MediumSingle correct
  3. 29 Jan 2024, Shift 1 · Q11If the value of the integral…HardSingle correct
  4. 1 Feb 2024, Shift 1 · Q27If ∫−π/2π/282cos⁡x dx(1+esin⁡x)(1+sin⁡4x)=απ+βlog⁡e(3+22)\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 α,β\alpha,\beta…HardNumerical value
  5. 4 Apr 2024, Shift 2 · Q10If the value of the integral ∫−11cos⁡αx1+3xdx\int_{-1}^{1}\frac{\cos\alpha x}{1+3^x}dx is 2π\frac{2}{\pi}. Then, a value of α\alpha isMediumSingle correct
  6. 27 Jun 2022, Shift 1 · Q10The value of the integral ∫−22∣x3+x∣(ex∣x∣+1) dx\int_{-2}^{2} \frac{|x^3+x|}{(e^{x|x|}+1)}\,dx is equal to :MediumSingle correct
  7. 25 Jun 2022, Shift 1 · Q2The value of ∫0πecos⁡xsin⁡x(1+cos⁡2x)(ecos⁡x+e−cos⁡x) dx\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
  8. 24 Jun 2022, Shift 2 · Q6The value of the integral ∫−π/2π/2dx(1+ex)(sin⁡6x+cos⁡6x)\int_{-\pi/2}^{\pi/2} \frac{dx}{(1+e^x)(\sin^6 x + \cos^6 x)} is equal toMediumSingle correct
  9. 26 Feb 2021, Shift 1 · Q69The value of ∫−π/2π/2cos⁡2x1+3x dx\int_{-\pi/2}^{\pi/2}\frac{\cos^2 x}{1+3^x}\,dx is :MediumSingle correct
  10. 26 Aug 2021, Shift 2 · Q67The value of ∫−π2π2(1+sin⁡2x1+πsin⁡x)dx\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{1+\sin^2 x}{1+\pi^{\sin x}}\right)\mathrm{d}x is :MediumSingle correct

Shifts: 26 Feb 2021, Shift 1, 26 Aug 2021, Shift 2, 24 Jun 2022, Shift 2, 25 Jun 2022, Shift 1, 27 Jun 2022, Shift 1, 29 Jan 2024, Shift 1, 1 Feb 2024, Shift 1, 4 Apr 2024, Shift 2, 2 Apr 2025, Shift 2, 6 Apr 2026, Shift 1.

Same topic

Other ideas in Definite Integral Properties

Definite Integral Properties has 19 ideas JEE Main has asked; 13 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas