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Saturday, 31 October

JEE Main · Maths · Integrals

Variable Limit Leibniz

JEE Main asked Variable Limit Leibniz 2 times in 2 of the 108 shifts Lumi analysed, all in 2022. It belongs to Leibniz Rule, in Integrals (Maths). In 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
1 of 8
First asked
2022
the only year
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.050.10’170’200’210.07’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 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
  • 20230 of 12
  • 20222 of 24
  • 20210 of 24
  • 20200 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.

  • Value from integral function and its derivative
  • Derivative of integral with variable limit

Difficulty

Easy 0Medium 1Hard 1

1 of the 2 questions had a numerical answer.

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. 30 Jun 2022, Shift 1 · Q25Let f(t)=∫0tex3(x8(x6+2x3+2)2)dxf(t) = \int_0^t e^{x^3}\left(\frac{x^8}{(x^6 + 2x^3 + 2)^2}\right) dx. If f(1)+f′(1)=αe−16f(1) + f'(1) = \alpha e - \frac{1}{6}, then the value of…HardNumerical value
  2. 27 Jun 2022, Shift 2 · Q8Let ff be a differentiable function in (0,π2)\left(0,\frac{\pi}{2}\right). If ∫cos⁡x1t2f(t) dt=sin⁡3x+cos⁡x\int_{\cos x}^{1}t^2f(t)\,dt=\sin^3x+\cos x, then…MediumSingle correct

Shifts: 27 Jun 2022, Shift 2, 30 Jun 2022, Shift 1.

Same topic

Other ideas in Leibniz Rule

Leibniz Rule has 5 ideas JEE Main has asked; 3 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas