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Saturday, 31 October

JEE Main · Maths · Integrals

Reciprocal Substitution (x = 1/t)

JEE Main asked Reciprocal Substitution (x = 1/t) 2 times in 2 of the 108 shifts Lumi analysed, in 2021 and 2026. It belongs to Definite Integral Properties, in Integrals (Maths). The longest wait between two years asking it was 5 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2021
last in 2026
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.03’210’220’230’240’250.11’26

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

Shift by shift

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

  • 20261 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20220 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: calculation.

  • Improper definite integral value
  • Definite integral using reciprocal substitution

Difficulty

Easy 0Medium 1Hard 1

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. 5 Apr 2026, Shift 1 · Q18The value of the integral ∫0∞log⁡e(x)x2+4 dx\int_0^{\infty} \frac{\log_e(x)}{x^2+4}\,dx is:HardSingle correct
  2. 26 Feb 2021, Shift 2 · Q80For x>0x>0, if f(x)=∫1xlog⁡et(1+t)dtf(x)=\int_1^x \frac{\log_e t}{(1+t)}dt, then f(e)+f(1e)f(e)+f\left(\frac{1}{e}\right) is equal to :MediumSingle correct

Shifts: 26 Feb 2021, Shift 2, 5 Apr 2026, 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