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Integral Calculus PYQs (previous year questions) for JEE Main: Integral Calculus (Mathematics) had 30 questions across the 11 official JEE Main papers we tagged (2016–2026), and appeared in 11 of them. Asked in 3 of 3 years. The concepts asked in the most papers: Area Under Curves, Definite Integrals, Definite Integrals with GIF.
Year-wise question count
Asked in 3 of 3 years.
| Year | Papers | Questions | Per paper |
|---|---|---|---|
| JEE Main 2026 | 9 | 24 | 2.7 |
| JEE Main 2017 | 1 | 3 | 3 |
| JEE Main 2016 | 1 | 3 | 3 |
Most-asked concepts
Sorted by the number of papers a concept appeared in.
| Concept | Questions | Papers | Years |
|---|---|---|---|
| Area Under Curves | 11 | 10 | 2026, 2017, 2016 |
| Definite Integrals | 11 | 8 | 2026 |
| Definite Integrals with GIF | 2 | 2 | 2026 |
| Indefinite Integration | 2 | 2 | 2026, 2016 |
| Definite Integration | 1 | 1 | 2017 |
| Indefinite Integrals | 1 | 1 | 2026 |
| Limit as Sum | 1 | 1 | 2016 |
| Reduction Formula | 1 | 1 | 2017 |
How to practise Integral Calculus PYQs
- Start with the concepts at the top of the table. They have come back the most.
- Solve one year’s Integral Calculus questions from the official PDF against the clock, then check the answer listed below.
- Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
- Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.
Questions by year
Each line gives the question number and paper, type, concept, our one-line summary and the official answer, with a link to the official PDF.
JEE Main2026
- Q.19 (2 April, shift 1) · MCQ · Definite Integrals with GIF: Integral of (e^x + e^-x)/[x]! from 0 to 3 (official answer: option 2) PDF
- Q.25 (2 April, shift 1) · Numerical · Definite Integrals: Sum of a log integral and a root integral (inverse functions); find alpha^2 (official answer: 192) PDF
- Q.17 (2 April, shift 2) · MCQ · Definite Integrals: Integral of sin^4 x + cos^4 x over 0 to 20 pi (official answer: option 3) PDF
- Q.19 (2 April, shift 2) · MCQ · Indefinite Integration: Partial fraction integral with given f(4); express f(7) as log of 2^a 3^b (official answer: option 3) PDF
- Q.24 (2 April, shift 2) · Numerical · Area Under Curves: Area bounded by a hyperbola and a line (official answer: 24) PDF
- Q.18 (4 April, shift 1) · MCQ · Area Under Curves: Area of region below y = pi - |x| and y = |x sin x| above x-axis (official answer: option 2) PDF
- Q.19 (4 April, shift 1) · MCQ · Definite Integrals with GIF: Integral of |sin x| + [x sin x] over [-2, 2]; find beta sin(beta/2) (official answer: option 2) PDF
- Q.18 (4 April, shift 2) · MCQ · Area Under Curves: Area bounded by parabolas x+3y²=0 and x+4y²=1 (official answer: option 3) PDF
- Q.20 (4 April, shift 2) · MCQ · Definite Integrals: Evaluate integral of cot⁻¹(1+x+x²) from 0 to 1 (official answer: option 4) PDF
- Q.16 (5 April, shift 1) · MCQ · Area Under Curves: Area of region xy≤27, 1≤y≤x² (official answer: option 2) PDF
- Q.18 (5 April, shift 1) · MCQ · Definite Integrals: Evaluate integral of ln x/(x²+4) from 0 to ∞ (official answer: option 2) PDF
- Q.20 (5 April, shift 1) · MCQ · Definite Integrals: Evaluate integral of (4−cosec²x)/cos⁴x from π/6 to π/3 (official answer: option 3) PDF
- Q.18 (5 April, shift 2) · MCQ · Definite Integrals: Minimum of f(a) from AP condition, then evaluate a definite integral (official answer: option 2) PDF
- Q.20 (5 April, shift 2) · MCQ · Indefinite Integrals: Given f''=g'' with initial values, find f(25)−g(25) (official answer: option 2) PDF
- Q.24 (5 April, shift 2) · Numerical · Area Under Curves: Max of f from a functional equation; area between x² and βx³ equals α² (official answer: 16) PDF
- Q.18 (6 April, shift 1) · MCQ · Definite Integrals: Integral of 32cos^4 x/(1+e^sin x) over -pi/4 to pi/4 (official answer: option 2) PDF
- Q.19 (6 April, shift 1) · MCQ · Area Under Curves: Area bounded by y<=6-x, y^2>=4x-3, y>=0, x>=0 (official answer: option 2) PDF
- Q.20 (6 April, shift 1) · MCQ · Area Under Curves: Bijective f, g define phi(x); area between x^2 and phi(x) on [0,1] (official answer: option 1) PDF
- Q.19 (6 April, shift 2) · MCQ · Area Under Curves: Area between parabola y = x^2 - 8x and line y = -x (official answer: option 1) PDF
- Q.20 (6 April, shift 2) · MCQ · Definite Integrals: Integral of (x^3+|x|+1)/(x^2+2|x|+1) over [-1,1] (official answer: option 2) PDF
- Q.16 (8 April, shift 2) · MCQ · Definite Integrals: Evaluate integral from 0 to 2 of a root-rational expression (official answer: option 3) PDF
- Q.18 (8 April, shift 2) · MCQ · Area Under Curves: Area bounded by composite function g, a line, y=0 and x=4 (official answer: option 1) PDF
- Q.19 (8 April, shift 2) · MCQ · Definite Integrals: Continuity fixes b; integral of |x^2+2x-3| over a range (official answer: option 4) PDF
- Q.22 (8 April, shift 2) · Numerical · Definite Integrals: Integral of cot(x-pi/3)cot(x+pi/3)+1 from pi/6 to pi/4 (official answer: 12) PDF
JEE Main2017
JEE Main2016
Integral Calculus in other exams
The same chapter in other official papers we tagged: JEE Advanced (39 questions).
Other Mathematics chapters
- Sets, Relations and Functions PYQs
- Complex Numbers and Quadratic Equations PYQs
- Matrices and Determinants PYQs
- Permutations and Combinations PYQs
- Binomial Theorem PYQs
- Sequences and Series PYQs
- Limits, Continuity and Differentiability PYQs
- Differential Equations PYQs
- Coordinate Geometry PYQs
- Three-Dimensional Geometry PYQs
- Vector Algebra PYQs
- Statistics and Probability PYQs
- Trigonometry PYQs
FAQ
How many Integral Calculus questions come in JEE Main?
In the official papers we tagged: 24 in 2026 (9 papers), 3 in 2017 (1 paper) and 3 in 2016 (1 paper). That is 30 questions in all, about 11% of Mathematics.
Which Integral Calculus topics repeat in JEE Main?
Asked in the most papers: Area Under Curves, Definite Integrals, Definite Integrals with GIF. The concept table lists every one with its count.
Are these official JEE Main questions?
Yes. Every question is from an official JEE Main paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.