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Saturday, 31 October

JEE Main · Maths · Integrals

Twin Trigonometric Integrals Substitution

JEE Main asked Twin Trigonometric Integrals Substitution 2 times in 2 of the 108 shifts Lumi analysed, in 2021 and 2022. It belongs to Integration by Substitution, in Integrals (Maths). The longest wait between two years asking it was 1 year.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2021
last in 2022
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021 and 2022. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200.03’210.04’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 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
  • 20221 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

Numerical value is the usual form. Skill tested: multi-step.

  • Integral with sin x +- cos x substitution
  • Indefinite integral of twin trig functions

Difficulty

Easy 0Medium 0Hard 2

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. 26 Jul 2022, Shift 2 · Q19The integral ∫(1−13)(cos⁡x−sin⁡x)(1+23sin⁡2x)dx\int\frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}}\sin 2x\right)}dx is equal toHardSingle correct
  2. 4 Aug 2021, Shift 1 · Q86If ∫(tan⁡x+cot⁡x)dx=atan⁡−1(tan⁡x−1btan⁡x)+C\int\left(\sqrt{\tan x}+\sqrt{\cot x}\right)dx=a\tan^{-1}\left(\frac{\tan x-1}{\sqrt{b\tan x}}\right)+\mathrm{C}, then the value of…HardNumerical value

Shifts: 4 Aug 2021, Shift 1, 26 Jul 2022, 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