Learn

Saturday, 31 October

JEE Main · Maths · Integrals

Modulus Function Interval Splitting

JEE Main asked Modulus Function Interval Splitting 6 times in 6 of the 108 shifts Lumi analysed, in 2020, 2021 and 2025. It belongs to Definite Integral Properties, in Integrals (Maths). The longest wait between two years asking it was 4 years. In 2020 and 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
3 of 8
First asked
2020
last in 2025
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170.17’200.10’210’220’230’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 3 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 20240 of 18
  • 20230 of 12
  • 20220 of 24
  • 20213 of 24
  • 20202 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: calculation.

  • Definite integral with modulus splitting
  • Definite integral with nested modulus

Difficulty

Easy 3Medium 2Hard 1

3 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. 8 Apr 2025, Shift 2 · Q19The integral ∫−132(∣π2xsin⁡(πx)∣)dx\int_{-1}^{\frac{3}{2}} \left(\left|\pi^2 x \sin(\pi x)\right|\right) dx is equal to :MediumSingle correct
  2. 26 Feb 2021, Shift 1 · Q88The value of the integral ∫0π∣sin⁡2x∣ dx\int_0^{\pi}|\sin 2x|\,dx is _________.EasyNumerical value
  3. 25 Feb 2021, Shift 2 · Q86The value of ∫−22∣3x2−3x−6∣ dx\int_{-2}^{2} |3x^2 - 3x - 6|\,dx is ________.MediumNumerical value
  4. 26 Aug 2021, Shift 1 · Q69The value of ∫−1/21/2((x+1x−1)2+(x−1x+1)2−2)1/2dx\int_{-1/\sqrt{2}}^{1/\sqrt{2}} \left(\left(\frac{x+1}{x-1}\right)^2 + \left(\frac{x-1}{x+1}\right)^2 - 2\right)^{1/2} dx…HardSingle correct
  5. 3 Sep 2020, Shift 1 · Q60∫−ππ∣π−∣x∣∣dx\int_{-\pi}^{\pi}|\pi-|x||dx is equal to :EasySingle correct
  6. 2 Sep 2020, Shift 1 · Q73The integral ∫02∣∣x−1∣−x∣dx\int_{0}^{2}\left||x-1|-x\right|dx is equal to ___________.EasyNumerical value

Shifts: 2 Sep 2020, Shift 1, 3 Sep 2020, Shift 1, 25 Feb 2021, Shift 2, 26 Feb 2021, Shift 1, 26 Aug 2021, Shift 1, 8 Apr 2025, Shift 2.

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