Explore: All CBSE Class 12 chapters · CBSE Class 12 Mathematics PYQs · CBSE Class 12 hub · Syllabus & pattern · Class 12 2026
Answer first
Integrals PYQs (previous year questions) for CBSE Class 12: Integrals (Mathematics) had 39 questions across the 50 official CBSE Class 12 papers we tagged (2016–2026), and appeared in 10 of them. Asked in 10 of 10 years. The concepts asked in the most papers: Definite Integrals, Properties of Definite Integrals, Integration by Substitution.
Year-wise question count
Asked in 10 of 10 years.
Most-asked concepts
Sorted by the number of papers a concept appeared in.
| Concept | Questions | Papers | Years |
|---|---|---|---|
| Definite Integrals | 8 | 6 | 2025, 2023, 2020, 2018, 2017, 2016 |
| Properties of Definite Integrals | 7 | 5 | 2026, 2024, 2023, 2022, 2019 |
| Indefinite Integrals | 5 | 5 | 2025, 2022, 2019, 2018, 2017 |
| Integration by Partial Fractions | 5 | 5 | 2024, 2023, 2019, 2018, 2017 |
| Integration by Substitution | 5 | 5 | 2026, 2025, 2024, 2022, 2019 |
| Integration by Parts | 4 | 3 | 2026, 2023, 2020 |
| Integration of Square Roots | 3 | 3 | 2026, 2017, 2016 |
| Integration of e^x Type | 1 | 1 | 2016 |
| Standard Integrals | 1 | 1 | 2020 |
How to practise Integrals PYQs
- Start with the concepts at the top of the table. They have come back the most.
- Solve one year’s Integrals 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, with a link to the official PDF.
CBSE Class 122026
- Q.8 (Mathematics (65/1/1)) · MCQ · Integration by Substitution: Find A when integral of 3ax/(b^2 + c^2 x^2) equals A log|...| PDF
- Q.9 (Mathematics (65/1/1)) · MCQ · Properties of Definite Integrals: Value of a definite integral of an odd function over symmetric limits PDF
- Q.26 (Mathematics (65/1/1)) · Short answer · Integration by Parts: Evaluate integral of x tan^-1 x PDF
- Q.27 (Mathematics (65/1/1)) · Short answer · Integration of Square Roots: Integrate sqrt((x + 2)/(x - 2)) PDF
- Q.28 (Mathematics (65/1/1)) · Short answer · Properties of Definite Integrals: Show I1 - 4 I2 = 0 for two definite integrals PDF
CBSE Class 122025
- Q.3 (Mathematics (65/1/1)) · MCQ · Definite Integrals: Value of integral of |x|/x from -1 to 1 PDF
- Q.10 (Mathematics (65/1/1)) · MCQ · Integration by Substitution: Find k in integral of 2^(1/x)/x^2 PDF
- Q.28 (Mathematics (65/1/1)) · Short answer · Indefinite Integrals: Integrate (x + sin x)/(1 + cos x) PDF
CBSE Class 122024
- Q.6 (Mathematics (65/1/1)) · MCQ · Properties of Definite Integrals: Equivalent form of the integral of f(x) from a to b PDF
- Q.23 (Mathematics (65/1/1)) · Very short answer · Integration by Substitution: Integrate x sqrt(1 + 2x) PDF
- Q.28 (Mathematics (65/1/1)) · Short answer · Integration by Partial Fractions: Integrate x^2 over (x^2 + 4)(x^2 + 9) PDF
- Q.33 (Mathematics (65/1/1)) · Long answer · Properties of Definite Integrals: Evaluate integral of (sin x + cos x)/(9 + 16 sin 2x) on 0 to pi/4 PDF
CBSE Class 122023
- Q.5 (Mathematics (65/1/1)) · MCQ · Integration by Parts: Find f(x) given its derivative is log x PDF
- Q.6 (Mathematics (65/1/1)) · MCQ · Definite Integrals: Evaluate a definite integral of a sec^2 expression PDF
- Q.26 (Mathematics (65/1/1)) · Short answer · Properties of Definite Integrals: Evaluate definite integral of log(sin x) - log(2 cos x) PDF
- Q.27 (Mathematics (65/1/1)) · Short answer · Integration by Partial Fractions: Integrate 1 over x(x - 1)(x - 2) PDF
- Q.31 (Mathematics (65/1/1)) · Short answer · Definite Integrals: Evaluate a definite integral of e^x sin x PDF
CBSE Class 122022
- Q.3 (Mathematics Term 2 (65/1/1)) · Short answer I · Indefinite Integrals: Find F(x) from its derivative sec^4 x / cosec^4 x and F(pi/4) PDF
- Q.9 (Mathematics Term 2 (65/1/1)) · Short answer II · Integration by Substitution: Integrate 1 over (sqrt x + cube root x) PDF
- Q.13 (Mathematics Term 2 (65/1/1)) · Long answer · Properties of Definite Integrals: Evaluate integral of x/(1 + sin x) from 0 to pi PDF
CBSE Class 122020
- Q.7 (Mathematics (65/1/1)) · MCQ · Definite Integrals: Value of a definite integral of sec^2 x PDF
- Q.17 (Mathematics (65/1/1)) · Very short answer · Integration by Parts: Integrate x^4 log x PDF
- Q.18 (Mathematics (65/1/1)) · Very short answer · Definite Integrals: Evaluate a definite integral of |2x - 1| PDF
- Q.20 (Mathematics (65/1/1)) · Very short answer · Standard Integrals: Integrate 1 over sqrt(9 - 4x^2) PDF
- Q.29 (Mathematics (65/1/1)) · Long answer I · Integration by Parts: Integrate sec^3 x PDF
CBSE Class 122019
- Q.7 (Mathematics (65/1/1)) · Short answer · Integration by Substitution: Integrate sec^2 x over (tan^2 x + 4) PDF
- Q.8 (Mathematics (65/1/1)) · Short answer · Indefinite Integrals: Integrate sqrt(1 - sin 2x) on a given interval PDF
- Q.19 (Mathematics (65/1/1)) · Long answer I · Integration by Partial Fractions: Integrate (3x + 5)/(x^2 + 3x - 18) PDF
- Q.20 (Mathematics (65/1/1)) · Long answer I · Properties of Definite Integrals: Prove f(x) to f(a-x) property and evaluate an x sin x integral PDF
CBSE Class 122018
- Q.9 (Mathematics (65/1)) · Short answer · Indefinite Integrals: Integrate (cos 2x + 2 sin^2 x)/cos^2 x PDF
- Q.18 (Mathematics (65/1)) · Long answer I · Integration by Partial Fractions: Integrate 2cos x over (1 - sin x)(1 + sin^2 x) PDF
- Q.27 (Mathematics (65/1)) · Long answer II · Definite Integrals: Evaluate integral of (sin x + cos x)/(16 + 9 sin 2x) over 0 to pi/4 PDF
CBSE Class 122017
- Q.3 (Mathematics (65/1)) · Very short answer · Indefinite Integrals: Integrate (sin^2 x - cos^2 x)/(sin x cos x) PDF
- Q.12 (Mathematics (65/1)) · Short answer · Integration of Square Roots: Integrate 1 over sqrt(5 - 8x - x^2) PDF
- Q.16 (Mathematics (65/1)) · Long answer I · Integration by Partial Fractions: Integrate cos theta over a product of sin/cos quadratics PDF
- Q.17 (Mathematics (65/1)) · Long answer I · Definite Integrals: Evaluate integral of x tan x/(sec x + tan x) from 0 to pi PDF
CBSE Class 122016
- Q.12 (Mathematics (65/1/N)) · Long answer I · Integration of e^x Type: Integrate (x-5)e^x over (x-3)^3 PDF
- Q.13 (Mathematics (65/1/N)) · Long answer I · Definite Integrals: Evaluate integral of x^2/(1+5^x) from -2 to 2 PDF
- Q.14 (Mathematics (65/1/N)) · Long answer I · Integration of Square Roots: Integrate (x+3) times sqrt(3-4x-x^2) PDF
Other Mathematics chapters
- Relations and Functions PYQs
- Inverse Trigonometric Functions PYQs
- Matrices PYQs
- Determinants PYQs
- Continuity and Differentiability PYQs
- Application of Derivatives PYQs
- Application of Integrals PYQs
- Differential Equations PYQs
- Vector Algebra PYQs
- Three Dimensional Geometry PYQs
- Linear Programming PYQs
- Probability PYQs
FAQ
How many Integrals questions come in CBSE Class 12?
In the official papers we tagged: 5 in 2026, 3 in 2025, 4 in 2024, 5 in 2023, 3 in 2022, 5 in 2020, 4 in 2019, 3 in 2018, 4 in 2017 and 3 in 2016. That is 39 questions in all, about 12% of Mathematics.
Which Integrals topics repeat in CBSE Class 12?
Asked in the most papers: Definite Integrals, Properties of Definite Integrals, Integration by Substitution. The concept table lists every one with its count.
Are these official CBSE Class 12 questions?
Yes. Every question is from an official CBSE Class 12 paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.