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Saturday, 31 October

JEE Main · Maths · Integrals

Composite Function Substitution

JEE Main asked Composite Function Substitution 6 times in 5 of the 108 shifts Lumi analysed, in 2021, 2024 and 2025. It belongs to Integration by Substitution, in Integrals (Maths). The longest wait between two years asking it was 3 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 5 shifts
Years
3 of 8
First asked
2021
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.10’210’220’230.09’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 3 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 in 18 shifts · 2025: 1 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
  • 20251 of 8
  • 202421 of 18
  • 20230 of 12
  • 20220 of 24
  • 20213 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: multi-step.

  • Indefinite integral with radical then evaluate constant
  • Integral of f' powers times f'' from tangent angles

Difficulty

Easy 0Medium 2Hard 4

1 of the 6 questions had a numerical answer.

Every question

All 6 questions

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

  1. 3 Apr 2025, Shift 1 · Q18Let f(x)=∫x33−x2 dxf(x) = \int x^3\sqrt{3 - x^2}\,dx. If 5f(2)=−45f(\sqrt{2}) = -4, then f(1)f(1) is equal toMediumSingle correct
  2. 30 Jan 2024, Shift 2 · Q12Let y=f(x)y = f(x) be a thrice differentiable function in (−5,5)(-5, 5). Let the tangents to the curve y=f(x)y = f(x) at (1,f(1))(1, f(1)) and (3,f(3))(3, f(3))…HardSingle correct
  3. 30 Jan 2024, Shift 2 · Q13Let f:R→Rf: \mathbb{R} \to \mathbb{R} be a function defined by f(x)=x(1+x4)1/4f(x) = \frac{x}{(1+x^4)^{1/4}}, and g(x)=f(f(f(f(x))))g(x) = f(f(f(f(x)))). Then,…HardSingle correct
  4. 18 Mar 2021, Shift 1 · Q73The integral ∫(2x−1)cos⁡(2x−1)2+54x2−4x+6 dx\int\dfrac{(2x-1)\cos\sqrt{(2x-1)^2+5}}{\sqrt{4x^2-4x+6}}\,dx is equal to : (where c is a constant of integration)MediumSingle correct
  5. 16 Mar 2021, Shift 2 · Q81For real numbers α,β,γ\alpha,\beta,\gamma and δ\delta, if…HardNumerical value
  6. 25 Feb 2021, Shift 1 · Q67The value of the integral…HardSingle correct

Shifts: 25 Feb 2021, Shift 1, 16 Mar 2021, Shift 2, 18 Mar 2021, Shift 1, 30 Jan 2024, Shift 2, 3 Apr 2025, 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