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Saturday, 31 October

JEE Main · Maths · Integrals

Trigonometric Substitution

JEE Main asked Trigonometric Substitution 3 times in 3 of the 108 shifts Lumi analysed, in 2020, 2023 and 2024. 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
3
in 3 shifts
Years
3 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, 2023 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170.08’200’210’220.07’230.05’240’250’26

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: 1 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
  • 20241 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: calculation.

  • Definite integral by trigonometric substitution
  • Indefinite integral with exponential of trig

Difficulty

Easy 0Medium 2Hard 1

Every question was multiple choice.

Every question

All 3 questions

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

  1. 6 Apr 2024, Shift 1 · Q11∫0π/4cos⁡2x sin⁡2x(cos⁡3x+sin⁡3x)2dx\int_0^{\pi/4}\frac{\cos^2 x\ \sin^2 x}{(\cos^3 x+\sin^3 x)^2}dx is equal toMediumSingle correct
  2. 10 Apr 2023, Shift 1 · Q8If I(x)=∫esin⁡2x(cos⁡xsin⁡2x−sin⁡x) dxI(x)=\int e^{\sin^2x}(\cos x\sin 2x-\sin x)\,dx and I(0)=1I(0)=1, then I(π3)I\left(\frac{\pi}{3}\right) is equal toHardSingle correct
  3. 3 Sep 2020, Shift 2 · Q61If the value of the integral ∫01/2x2(1−x2)3/2dx\int_0^{1/2} \frac{x^2}{(1 - x^2)^{3/2}} dx is k6\frac{k}{6}, then k is equal to :MediumSingle correct

Shifts: 3 Sep 2020, Shift 2, 10 Apr 2023, Shift 1, 6 Apr 2024, 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