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Saturday, 31 October

JEE Main · Maths · Integrals

Implicit Derivative Recognition

JEE Main asked Implicit Derivative Recognition 2 times in 2 of the 108 shifts Lumi analysed, in 2020 and 2023. It belongs to Integration by Substitution, in Integrals (Maths). The longest wait between two years asking it was 3 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2020
last in 2023
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170.08’200’210’220.07’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 in 24 shifts · 2023: 1 in 12 shifts · 2024: 0 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
  • 20240 of 18
  • 20231 of 12
  • 20220 of 24
  • 20210 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: multi-step.

  • Indefinite integral by recognising derivative of xe^x
  • Definite integral of exact derivative of product

Difficulty

Easy 0Medium 0Hard 2

Every question was multiple choice.

Every question

All 2 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 2023, Shift 1 · Q11Let I(x)=∫(x+1)x(1+xex)2dxI(x)=\int\frac{(x+1)}{x(1+xe^x)^2}dx, x>0x>0. If lim⁡x→∞I(x)=0\lim_{x\to\infty}I(x)=0, then I(1)I(1) is equal toHardSingle correct
  2. 4 Sep 2020, Shift 2 · Q61The integral ∫π/6π/3tan⁡3x⋅sin⁡23x (2sec⁡2x⋅sin⁡23x+3tan⁡x⋅sin⁡6x) dx\int_{\pi/6}^{\pi/3} \tan^3 x \cdot \sin^2 3x \,(2\sec^2 x \cdot \sin^2 3x + 3\tan x \cdot \sin 6x)\,dx is equal to :HardSingle correct

Shifts: 4 Sep 2020, Shift 2, 8 Apr 2023, Shift 1.

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