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Saturday, 31 October

JEE Main · Maths · Integrals

Reduction Formulae in Definite Integrals

JEE Main asked Reduction Formulae in Definite Integrals 6 times in 6 of the 108 shifts Lumi analysed, in 2021, 2022, 2023 and 2024. It belongs to Definite Integral Properties, in Integrals (Maths). The longest wait between two years asking it was 1 year. In 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
4 of 8
First asked
2021
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.03’210.04’220.07’230.14’240’250’26

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

Shift by shift

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

  • 20260 of 9
  • 20250 of 8
  • 20243 of 18
  • 20231 of 12
  • 20221 of 24
  • 20211 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 with reduction relation
  • Reduction relation for definite integral

Difficulty

Easy 0Medium 1Hard 5

1 of the 6 questions had a numerical answer.

Every question

All 6 questions

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

  1. 1 Feb 2024, Shift 2 · Q10If ∫0π3cos⁡4x dx=aπ+b3\int_0^{\frac{\pi}{3}}\cos^4x\,dx=a\pi+b\sqrt{3}, where aa and bb are rational numbers, then 9a+8b9a+8b is equal to :MediumSingle correct
  2. 8 Apr 2024, Shift 1 · Q11The value of k∈Nk\in\mathbb{N} for which the integral In=∫01(1−xk)ndxI_n=\int_0^1(1-x^k)^n dx, n∈Nn\in\mathbb{N}, satisfies 147I20=148I21147I_{20}=148I_{21} isHardSingle correct
  3. 6 Apr 2024, Shift 1 · Q25Let rk=∫01(1−x7)kdx∫01(1−x7)k+1dxr_k=\frac{\int_0^1\left(1-x^7\right)^k dx}{\int_0^1\left(1-x^7\right)^{k+1}dx}, k∈Nk \in \mathbb{N}. Then the value of…HardNumerical value
  4. 13 Apr 2023, Shift 2 · Q10The value of…HardSingle correct
  5. 25 Jun 2022, Shift 2 · Q12If bn=∫0π2cos⁡2nxsin⁡x dxb_n = \int_0^{\frac{\pi}{2}} \frac{\cos^2 nx}{\sin x}\,dx, n∈Nn \in \mathbb{N}, thenHardSingle correct
  6. 25 Feb 2021, Shift 2 · Q64If In=∫π/4π/2cot⁡nx dxI_n = \int_{\pi/4}^{\pi/2} \cot^n x \, dx, then :HardSingle correct

Shifts: 25 Feb 2021, Shift 2, 25 Jun 2022, Shift 2, 13 Apr 2023, Shift 2, 1 Feb 2024, Shift 2, 6 Apr 2024, Shift 1, 8 Apr 2024, 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