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Friday, 9 October

JEE Main Maths · Integrals

Greatest Integer Function Integrals

Greatest Integer Function Integrals (Integrals) was asked 9 times in 9 JEE Main shifts, 2021–2026, out of the 42 shifts Lumi analysed. 4 of the 9 had a numerical answer.

Times asked
9
in 9 shifts
Years
2021–2026
Usual format
Single correct
Calculation
Pattern
Asked most years
repeats across shifts

How it is asked

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

Difficulty

Easy 0Medium 6Hard 3

Where it sits

Chapter: Integrals. Topic: Definite Integral Properties, 30 questions over 12 ideas.

Other repeat ideas in this topic

Every time it came

All 9 questions

Newest first, each with its options and official answer.

  1. 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
  2. 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
  3. 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
  4. 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
  5. 6 Apr 2024, Shift 2 · Q25Let [t][t] denote the largest integer less than or equal to tt. If…HardNumerical value
  6. 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
  7. 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
  8. 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
  9. 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