Learn

Friday, 9 October

JEE Main Maths · Differential Equations

Solving Integral Equations

Solving Integral Equations (Differential Equations) was asked 4 times in 4 JEE Main shifts, 2024–2026, out of the 42 shifts Lumi analysed. 1 of the 4 had a numerical answer.

Times asked
4
in 4 shifts
Years
2024–2026
Usual format
Single correct
Multi-step
Pattern
New since 2024
repeats across shifts

How it is asked

  • Derivatives from integral equation
  • Solve integral equation for f

Difficulty

Easy 0Medium 1Hard 3

Where it sits

Chapter: Differential Equations. Topic: Leibniz Rule, 5 questions over 2 ideas.

Every time it came

All 4 questions

Newest first, each with its options and official answer.

  1. 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
  2. 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
  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. 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