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Integral Calculus PYQs (previous year questions) for JEE Advanced: Integral Calculus (Mathematics) had 39 questions across the 22 official JEE Advanced papers we tagged (2016–2026), and appeared in 18 of them. Asked in 11 of 11 years. The concepts asked in the most papers: Definite Integrals, Area Under Curves, Limit as a Sum.
Year-wise question count
Asked in 11 of 11 years, with 2 papers each year.
Most-asked concepts
Sorted by the number of papers a concept appeared in.
| Concept | Questions | Papers | Years |
|---|---|---|---|
| Definite Integrals | 19 | 15 | 2026, 2025, 2024, 2022, 2021, 2020, 2019, 2018, 2017, 2016 |
| Area Under Curves | 13 | 11 | 2026, 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016 |
| Limit as a Sum | 2 | 2 | 2018, 2016 |
| Greatest Integer Function | 1 | 1 | 2021 |
| Integral Equations | 1 | 1 | 2018 |
| Intermediate Value Theorem | 1 | 1 | 2017 |
| Leibniz Rule | 1 | 1 | 2017 |
| Limit of Sum | 1 | 1 | 2019 |
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 Advanced2026
- Q.4 (Paper 2) · MCQ · Definite Integrals: Value of a definite integral of a rational function of 3 to the x (official answer: B) PDF
- Q.16 (Paper 2) · Numerical · Area Under Curves: Expression from the area between two curves over chosen intersections (official answer: 2.4–2.6) PDF
- Q.18 (Paper 2) · Numerical · Area Under Curves: Area of the region common to two ellipses (official answer: 0.74–0.76) PDF
JEE Advanced2025
JEE Advanced2024
- Q.2 (Paper 2) · MCQ · Area Under Curves: Area of a region bounded by two parabolas and a line (official answer: B) PDF
- Q.13 (Paper 2) · Integer · Definite Integrals: Count solutions involving the integral of a piecewise function (official answer: 5) PDF
- Q.16 (Paper 2) · Numerical · Definite Integrals: Value of a combination of integrals of sin^2 x and a quadratic (official answer: 0) PDF
- Q.17 (Paper 2) · Numerical · Definite Integrals: Scaled integral of the product of sin^2 x and a quadratic (official answer: 0.24–0.26) PDF
JEE Advanced2023
JEE Advanced2022
- Q.9 (Paper 1) · MSQ · Definite Integrals: Values of a satisfying an equation given by a log-type definite integral (official answer: C, D) PDF
- Q.3 (Paper 2) · Integer · Definite Integrals: Greatest integer of the sum of two definite integrals (official answer: 5) PDF
- Q.8 (Paper 2) · Integer · Area Under Curves: Area under the minimum of two functions; find 9 alpha (official answer: 6) PDF
JEE Advanced2021
- Q.2 (Paper 1) · MCQ · Area Under Curves: Area of a region bounded by linear inequalities PDF
- Q.3 (Paper 2) · MSQ · Definite Integrals: Existence of roots and a limit for a function with given integral PDF
- Q.11 (Paper 2) · Numerical · Definite Integrals: Value of an integral of sin^2 x on [pi/8, 3pi/8] PDF
- Q.12 (Paper 2) · Numerical · Definite Integrals: Value of an integral of sin^2 x times |4x - pi| PDF
- Q.19 (Paper 2) · Integer · Greatest Integer Function: Integral of floor of a square-root expression PDF
JEE Advanced2020
- Q.3 (Paper 1) · MCQ · Area Under Curves: Area in the first quadrant bounded by two exponential curves PDF
- Q.12 (Paper 1) · MSQ · Definite Integrals: Which definite integral inequalities hold PDF
- Q.17 (Paper 2) · Numerical · Definite Integrals: f(0) from an integral condition involving f and its integral PDF
JEE Advanced2019
- Q.4 (Paper 1) · MCQ · Area Under Curves: Area of region bounded by xy <= 8 and 1 <= y <= x^2 (official answer: A) PDF
- Q.17 (Paper 1) · Numerical · Definite Integrals: Value of a definite integral with exponential and trig terms (official answer: 4) PDF
- Q.6 (Paper 2) · MSQ · Limit of Sum: Values of a for which a limit of sums equals 54 (official answer: A, D) PDF
- Q.13 (Paper 2) · Numerical · Definite Integrals: Integral involving powers of root cos and root sin (official answer: 0.5) PDF
JEE Advanced2018
- Q.6 (Paper 1) · MSQ · Integral Equations: Properties of f defined by an integral equation PDF
- Q.11 (Paper 1) · Numerical · Limit as a Sum: Greatest integer of the limit of a product-root sequence PDF
- Q.14 (Paper 1) · Numerical · Area Under Curves: Exponent n so area between line and y=x^n is 30% of triangle PDF
- Q.7 (Paper 2) · Numerical · Definite Integrals: Evaluate a definite integral with fractional powers PDF
JEE Advanced2017
- Q.40 (Paper 1) · MSQ · Intermediate Value Theorem: Functions with a zero in (0,1) for a continuous f (official answer: A, B) PDF
- Q.45 (Paper 1) · Integer · Definite Integrals: Limit of an integral-defined function near zero (official answer: 2) PDF
- Q.44 (Paper 2) · MSQ · Leibniz Rule: Derivative of an integral with variable limits at a point (official answer: Marks to all) PDF
- Q.49 (Paper 2) · MSQ · Area Under Curves: Line x=a bisecting area between y=x^2 and y=x (official answer: B, C) PDF
- Q.50 (Paper 2) · MSQ · Definite Integrals: Bounds on a sum of integrals compared with log 99 (official answer: B, D) PDF
JEE Advanced2016
- Q.52 (Paper 1) · Integer · Definite Integrals: Number of x in [0,1] where an integral equals a linear function (official answer: 1) PDF
- Q.40 (Paper 2) · MCQ · Definite Integrals: Integral of x^2 cos x over 1+e^x on a symmetric interval (official answer: A) PDF
- Q.41 (Paper 2) · MCQ · Area Under Curves: Area bounded by a root curve and two lines (official answer: C) PDF
- Q.43 (Paper 2) · MSQ · Limit as a Sum: Properties of f defined as a limit of a product (official answer: B, C) PDF
Integral Calculus in other exams
The same chapter in other official papers we tagged: JEE Main (30 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 Advanced?
In the official papers we tagged: 3 in 2026, 2 in 2025, 4 in 2024, 2 in 2023, 3 in 2022, 5 in 2021, 3 in 2020, 4 in 2019, 4 in 2018, 5 in 2017 and 4 in 2016 (2 papers each year). That is 39 questions in all, about 10% of Mathematics.
Which Integral Calculus topics repeat in JEE Advanced?
Asked in the most papers: Definite Integrals, Area Under Curves, Limit as a Sum. The concept table lists every one with its count.
Are these official JEE Advanced questions?
Yes. Every question is from an official JEE Advanced paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.