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Saturday, 31 October

JEE Main · Maths · Integrals

Greatest Integer Function Integrals

JEE Main asked Greatest Integer Function Integrals 29 times in 28 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Definite Integral Properties, in Integrals (Maths). The longest wait between two years asking it was 1 year. In 2021, 2022, 2023, 2024, 2025 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
29
in 28 shifts
Years
7 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.20.40’170.08’200.38’210.28’220.21’230.09’240.25’250.22’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 11 in 24 shifts · 2022: 8 in 24 shifts · 2023: 3 in 12 shifts · 2024: 2 in 18 shifts · 2025: 2 in 8 shifts · 2026: 2 in 9 shifts.

Shift by shift

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

  • 20262 of 9
  • 20252 of 8
  • 20242 of 18
  • 20233 of 12
  • 202227 of 24
  • 202111 of 24
  • 20201 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: calculation.

  • Definite integral with greatest integer function
  • Definite integral with greatest integer

Difficulty

Easy 0Medium 16Hard 13

11 of the 29 questions had a numerical answer.

Every question

All 29 questions

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

  1. 4 Apr 2026, Shift 1 · Q19Let ∫−22(∣sin⁡x∣+[xsin⁡x])dx=2(3−cos⁡2)+β\int_{-2}^{2}\left(|\sin x|+[x\sin x]\right)dx=2(3-\cos 2)+\beta, where [⋅][\cdot] is the greatest integer function. Then…HardSingle correct
  2. 2 Apr 2026, Shift 1 · Q19Let [⋅][\cdot] denote the greatest integer function. Then the value of ∫03(ex+e−x[x]!)dx\int_0^3\left(\frac{e^x+e^{-x}}{[x]!}\right)dx is :MediumSingle correct
  3. 3 Apr 2025, Shift 1 · Q19Let the domain of the function f(x)=log⁡2log⁡4log⁡6(3+4x−x2)f(x) = \log_2 \log_4 \log_6 (3 + 4x - x^2) be (a,b)(a, b). If…HardSingle correct
  4. 2 Apr 2025, Shift 1 · Q23Let [⋅][\cdot] denote the greatest integer function. If ∫0e3[1ex−1]dx=α−log⁡e2\int_0^{e^3}\left[\frac{1}{e^{x-1}}\right]dx=\alpha-\log_e2, then α3\alpha^3 is…MediumNumerical value
  5. 30 Jan 2024, Shift 1 · Q25The value of 9∫09[10xx+1]dx9\int_0^9\left[\sqrt{\frac{10x}{x+1}}\right]dx, where [t][t] denotes the greatest integer less than or equal to tt, is…HardNumerical value
  6. 6 Apr 2024, Shift 2 · Q25Let [t][t] denote the largest integer less than or equal to tt. If…HardNumerical value
  7. 11 Apr 2023, Shift 2 · Q11Let the function f:[0,2]→Rf : [0, 2] \to \mathbb{R} be defined as…HardSingle correct
  8. 8 Apr 2023, Shift 2 · Q26Let [t][t] denote the greatest integer function. If ∫02.4[x2] dx=α+β2+γ3+δ5\int_0^{2.4}[x^2]\,dx = \alpha + \beta\sqrt{2} + \gamma\sqrt{3} + \delta\sqrt{5},…MediumNumerical value
  9. 8 Apr 2023, Shift 1 · Q24Let [t][t] denote the greatest integer ≤t\le t. Then 2π∫π/65π/6(8[cosec⁡x]−5[cot⁡x]) dx\frac{2}{\pi}\int_{\pi/6}^{5\pi/6}(8[\operatorname{cosec}x]-5[\cot x])\,dx is equal…HardNumerical value
  10. 29 Jun 2022, Shift 1 · Q17∫05cos⁡(π(x−[x2]))dx\int_0^5 \cos\left(\pi\left(x - \left[\frac{x}{2}\right]\right)\right)dx, where [t][t] denotes greatest integer less than or equal to…MediumSingle correct
  11. 28 Jun 2022, Shift 1 · Q7Let [t][t] denote the greatest integer less than or equal to tt. Then, the value of the integral ∫01[−8x2+6x−1] dx\int_0^1[-8x^2+6x-1]\,dx is equal toHardSingle correct
  12. 27 Jun 2022, Shift 2 · Q9The integral ∫0117[1x] dx\int_0^1\frac{1}{7^{\left[\frac{1}{x}\right]}}\,dx, where [⋅][\cdot] denotes the greatest integer function, is equal toHardSingle correct
  13. 29 Jul 2022, Shift 2 · Q5If [t][t] denotes the greatest integer ≤t\leq t, then the value of ∫01[2x−∣3x2−5x+2∣+1]dx\int_0^1\left[2x-\left|3x^2-5x+2\right|+1\right]dx is :HardSingle correct
  14. 27 Jul 2022, Shift 2 · Q9∫02(∣2x2−3x∣+[x−12])dx\int_0^2 \left(\left|2x^2 - 3x\right| + \left[x - \frac{1}{2}\right]\right) dx, where [t] is the greatest integer function, is equal to :MediumSingle correct
  15. 27 Jul 2022, Shift 2 · Q27Let f(x)=min⁡{[x−1],[x−2],…,[x−10]}f(x) = \min\{[x - 1], [x - 2], \ldots, [x - 10]\} where [t] denotes the greatest integer ≤\leq t. Then…HardNumerical value
  16. 27 Jul 2022, Shift 1 · Q7Let f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} be a function defined as f(x)=asin⁡(π[x]2)+[2−x]f(x) = a\sin\left(\dfrac{\pi[x]}{2}\right) + [2-x],…MediumSingle correct
  17. 25 Jul 2022, Shift 2 · Q9Let [t][t] denote the greatest integer less than or equal to tt. Then the value of the integral…MediumSingle correct
  18. 17 Mar 2021, Shift 2 · Q66If the integral ∫010[sin⁡2πx]ex−[x]dx=αe−1+βe−12+γ\int_0^{10}\frac{[\sin 2\pi x]}{e^{x-[x]}}dx=\alpha e^{-1}+\beta e^{-\frac{1}{2}}+\gamma, where α,β,γ\alpha, \beta, \gamma…HardSingle correct
  19. 17 Mar 2021, Shift 1 · Q85If [ ⋅\cdot ] represents the greatest integer function, then the value of…HardNumerical value
  20. 16 Mar 2021, Shift 2 · Q74Consider the integral I=∫010[x] e[x]ex−1 dxI=\int_0^{10}\frac{[x]\,e^{[x]}}{e^{x-1}}\,dx, where [x][x] denotes the greatest integer less than or equal to xx.…MediumSingle correct
  21. 25 Feb 2021, Shift 1 · Q68The value of ∫−11x2e[x3]dx\int_{-1}^{1} x^2 e^{[x^3]}dx, where [t] denotes the greatest integer ≤\leq t, is :MediumSingle correct
  22. 24 Feb 2021, Shift 2 · Q65The value of the integral, ∫13[x2−2x−2]dx\int_{1}^{3}[x^2-2x-2]\mathrm{d}x, where [x][x] denotes the greatest integer less than or equal to xx, is :MediumSingle correct
  23. 24 Feb 2021, Shift 1 · Q87If ∫−aa(∣x∣+∣x−2∣)dx=22\int_{-a}^{a}(|x| + |x - 2|)dx = 22, (a>2a > 2) and [x][x] denotes the greatest integer ≤x\le x, then ∫a−a(x+[x])dx\int_{a}^{-a}(x + [x])dx is…MediumNumerical value
  24. 31 Aug 2021, Shift 2 · Q69If [x][x] is the greatest integer ≤x\le x, then π2∫02(sin⁡πx2)(x−[x])[x] dx\pi^2 \int_0^2 \left(\sin\frac{\pi x}{2}\right)(x-[x])^{[x]}\,\mathrm{d}x is equal to :HardSingle correct
  25. 31 Aug 2021, Shift 1 · Q84Let [t] denote the greatest integer ≤\leq t. Then the value of 8⋅∫−121([2x]+∣x∣) dx8\cdot\int_{-\frac{1}{2}}^{1}([2x]+|x|)\,dx is __________.MediumNumerical value
  26. 26 Aug 2021, Shift 2 · Q74If the value of the integral ∫05x+[x]ex−[x] dx=αe−1+β\int_0^5\frac{x+[x]}{\mathrm{e}^{x-[x]}}\,\mathrm{d}x=\alpha\mathrm{e}^{-1}+\beta, where…MediumSingle correct
  27. 3 Aug 2021, Shift 2 · Q84If [x][x] denotes the greatest integer ≤x\le x, then the value of ∫−24∣[x]−x∣dx\int_{-2}^{4}\left|[x] - x\right|dx is ‾\underline{\hspace{2em}}.MediumNumerical value
  28. 3 Aug 2021, Shift 1 · Q70∫12[x2−1]+[x2+1] dx\int_1^2 [x^2 - 1] + [x^2 + 1]\, dx is equal to ([t][t] denotes the greatest integer ≤t\leq t)MediumSingle correct
  29. 2 Sep 2020, Shift 2 · Q74Let [t] denote the greatest integer less than or equal to t. Then the value of ∫12∣2x−[3x]∣ dx\int_1^2 |2x-[3x]|\,dx is ________.MediumNumerical value

Shifts: 2 Sep 2020, Shift 2, 24 Feb 2021, Shift 2, 24 Feb 2021, Shift 1, 25 Feb 2021, Shift 1, 16 Mar 2021, Shift 2, 17 Mar 2021, Shift 2, 17 Mar 2021, Shift 1, 3 Aug 2021, Shift 2, 3 Aug 2021, Shift 1, 26 Aug 2021, Shift 2, 31 Aug 2021, Shift 2, 31 Aug 2021, Shift 1, 27 Jun 2022, Shift 2, 28 Jun 2022, Shift 1, 29 Jun 2022, Shift 1, 25 Jul 2022, Shift 2, 27 Jul 2022, Shift 2, 27 Jul 2022, Shift 1, 29 Jul 2022, Shift 2, 8 Apr 2023, Shift 2, 8 Apr 2023, Shift 1, 11 Apr 2023, Shift 2, 30 Jan 2024, Shift 1, 6 Apr 2024, Shift 2, 2 Apr 2025, Shift 1, 3 Apr 2025, Shift 1, 2 Apr 2026, Shift 1, 4 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