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Saturday, 31 October

JEE Main · Maths · Differential Equations

Solving Integral Equations

JEE Main asked Solving Integral Equations 11 times in 11 of the 108 shifts Lumi analysed, in 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Leibniz Rule, in Differential Equations (Maths). The longest wait between two years asking it was 1 year. In 2022, 2023, 2024 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
11
in 11 shifts
Years
6 of 8
First asked
2021
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170’200.03’210.11’220.14’230.09’240.13’250.22’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 3 in 24 shifts · 2023: 2 in 12 shifts · 2024: 2 in 18 shifts · 2025: 1 in 8 shifts · 2026: 2 in 9 shifts.

Shift by shift

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

  • 20262 of 9
  • 20251 of 8
  • 20242 of 18
  • 20232 of 12
  • 20223 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: multi-step.

  • Integral equation to differential equation
  • Solve integral equation for function value

Difficulty

Easy 0Medium 6Hard 5

5 of the 11 questions had a numerical answer.

Every question

All 11 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 2 · Q19Let f:[1,∞)→Rf:[1,\infty)\to\mathbf{R} be a differentiable function defined as f(x)=∫1xf(t) dt+(1−x)(log⁡ex−1)+ef(x)=\int_1^x f(t)\,dt+(1-x)(\log_e x-1)+e. Then the value of…HardSingle correct
  2. 4 Apr 2026, Shift 2 · Q25Let ff be a twice differentiable function such that f(x)=∫0xtan⁡(t−x) dt−∫0xf(t)tan⁡t dtf(x)=\int_0^x\tan(t-x)\,dt-\int_0^x f(t)\tan t\,dt,…HardNumerical value
  3. 2 Apr 2025, Shift 2 · Q20Let f:[1,∞)→[2,∞)f : [1, \infty) \to [2, \infty) be a differentiable function. If 10∫1xf(t) dt=5xf(x)−x5−910\int_1^x f(t)\,\mathrm{d}t = 5xf(x) - x^5 - 9 for all…MediumSingle correct
  4. 1 Feb 2024, Shift 2 · Q24Let f:(0,∞)→Rf:(0,\infty)\to\mathbf{R} and F(x)=∫0xtf(t) dtF(x)=\int_0^x t f(t)\,dt. If F(x2)=x4+x5F(x^2)=x^4+x^5, then ∑r=112f(r2)\sum_{r=1}^{12}f(r^2) is equal to ________.MediumNumerical value
  5. 9 Apr 2024, Shift 2 · Q13Let ∫0x1−(y′(t))2 dt=∫0xy(t) dt, 0≤x≤3, y≥0, y(0)=0\int_0^x\sqrt{1-(y'(t))^2}\,dt=\int_0^x y(t)\,dt,\ 0\le x\le 3,\ y\ge0,\ y(0)=0. Then at x=2x=2, y′′+y+1y''+y+1 is equal toHardSingle correct
  6. 10 Apr 2023, Shift 2 · Q11Let ff be a continuous function satisfying ∫0t2(f(x)+x2) dx=43t3, ∀t>0\int_0^{t^2} (f(x) + x^2)\, dx = \frac{4}{3}t^3,\ \forall t > 0. Then…MediumSingle correct
  7. 10 Apr 2023, Shift 1 · Q9Let ff be a differentiable function such that x2f(x)−x=4∫0xtf(t) dtx^2f(x)-x=4\int_0^x tf(t)\,dt, f(1)=23f(1)=\frac{2}{3}. Then 18f(3)18f(3) is equal toMediumSingle correct
  8. 29 Jun 2022, Shift 2 · Q7Let ff be a real valued continuous function on [0,1][0, 1] and f(x)=x+∫01(x−t)f(t) dtf(x) = x + \int_0^1 (x - t) f(t)\,dt. Then, which of the following points…MediumSingle correct
  9. 27 Jul 2022, Shift 2 · Q28Let f be a differentiable function satisfying f(x)=23∫03f(λ2x3)dλf(x) = \frac{2}{\sqrt{3}} \int_0^{\sqrt{3}} f\left(\frac{\lambda^2 x}{3}\right) d\lambda,…HardNumerical value
  10. 25 Jul 2022, Shift 2 · Q26Let ff be a twice differentiable function on R\mathbb{R}. If f′(0)=4f'(0)=4 and…HardNumerical value
  11. 31 Aug 2021, Shift 1 · Q85If x ϕ(x)=∫5x(3t2−2ϕ′(t)) dtx\,\phi(x)=\int_5^x(3t^2-2\phi'(\mathrm{t}))\,\mathrm{dt}, x>−2x>-2, and ϕ(0)=4\phi(0)=4, then ϕ(2)\phi(2) is __________.MediumNumerical value

Shifts: 31 Aug 2021, Shift 1, 29 Jun 2022, Shift 2, 25 Jul 2022, Shift 2, 27 Jul 2022, Shift 2, 10 Apr 2023, Shift 2, 10 Apr 2023, Shift 1, 1 Feb 2024, Shift 2, 9 Apr 2024, Shift 2, 2 Apr 2025, Shift 2, 4 Apr 2026, Shift 2, 5 Apr 2026, Shift 2.

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