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Saturday, 31 October

JEE Main · Maths · Integrals

Fractional Powers LCM Substitution

JEE Main asked Fractional Powers LCM Substitution 5 times in 5 of the 108 shifts Lumi analysed, in 2020, 2021, 2023 and 2024. It belongs to Integration by Substitution, in Integrals (Maths). The longest wait between two years asking it was 2 years. In 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
4 of 8
First asked
2020
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170.08’200.03’210’220.07’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 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
  • 20242 of 18
  • 20231 of 12
  • 20220 of 24
  • 20211 of 24
  • 20201 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: multi-step.

  • Definite integral with fractional powers
  • Integral by mobius-type substitution

Difficulty

Easy 0Medium 1Hard 4

3 of the 5 questions had a numerical answer.

Every question

All 5 questions

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

  1. 31 Jan 2024, Shift 1 · Q27If the integral 525∫0π2sin⁡2xcos⁡112x(1+cos⁡52x)12dx525\int_0^{\frac{\pi}{2}}\sin2x\cos^{\frac{11}{2}}x\left(1+\cos^{\frac{5}{2}}x\right)^{\frac{1}{2}}dx is equal to…HardNumerical value
  2. 8 Apr 2024, Shift 2 · Q26If ∫1(x−1)4(x+3)65 dx=A(αx−1βx+3)B+C\int \frac{1}{\sqrt[5]{(x-1)^4(x+3)^6}}\,dx = A\left(\frac{\alpha x - 1}{\beta x + 3}\right)^B + C, where C is the constant of…HardNumerical value
  3. 12 Apr 2023, Shift 1 · Q27Let I(x)=∫x+7x dxI(x)=\int\sqrt{\frac{x+7}{x}}\,dx and I(9)=12+7log⁡e7I(9)=12+7\log_e 7. If I(1)=α+7log⁡e(1+22)I(1)=\alpha+7\log_e(1+2\sqrt{2}), then α4\alpha^4 is equal to…HardNumerical value
  4. 27 Aug 2021, Shift 2 · Q70The value of the integral ∫01x dx(1+x)(1+3x)(3+x)\int_0^1 \frac{\sqrt{x}\, dx}{(1+x)(1+3x)(3+x)} is :HardSingle correct
  5. 4 Sep 2020, Shift 1 · Q62Let f(x)=∫x(1+x)2 dxf(x) = \int \frac{\sqrt{x}}{(1+x)^2}\,\mathrm{d}x (x≥0)(x \ge 0). Then f(3)−f(1)f(3) - f(1) is equal to :MediumSingle correct

Shifts: 4 Sep 2020, Shift 1, 27 Aug 2021, Shift 2, 12 Apr 2023, Shift 1, 31 Jan 2024, Shift 1, 8 Apr 2024, Shift 2.

Same topic

Other ideas in Integration by Substitution

Integration by Substitution has 27 ideas JEE Main has asked; 12 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas