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Integral calculus is an important and high-weightage topic that is asked both in the JEE Main and JEE Advanced Exam. The topic carries approximately 12-14% weightage and candidates can expect 4 to 5 questions from this section in the exam.
The integral calculus section focuses on finding areas under curves, differential equations, and evaluating integrals. The most asked topics in the Integral calculus section are definite integrals, area under curves, and differential equations.
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Listed below are the previous year's questions of Integral Calculus asked in JEE Main with detailed solutions.
Question 1:
Question 2:
Question 3:
Question 4:
Question 5:
Question 6:
Question 7:
Question 8:
Question 9:
Question 10:
JEE Main Mathematics Paper Pattern
The NTA has updated the JEE Main Chemistry Exam Pattern for 2025. Earlier, section B allowed candidates to attempt only 5 out of 10 NVQs, but now all 5 are compulsory.
The detailed exam pattern for JEE Main Mathematics is given below:
| Aspect | Details |
|---|---|
| Mode of Exam | Online Computer-Based Test (CBT) |
| Language of Exam | English, Hindi, Assamese, Bengali, Gujarati, Kannada, Malayalam, Marathi, Odia, Punjabi, Tamil, Telugu, and Urdu |
| Types of Questions | Section A: Multiple Choice Questions (MCQs)Section B: Numerical Value-Based Questions (NVQs) |
| Total Number of Questions | 25 QuestionsSection A: 20 MCQsSection B: 5 NVQs (All mandatory) |
| Marking Scheme | Correct Answer: +4 marksIncorrect Answer: -1 mark (applies to both MCQs and NVQs)Unanswered/Marked for Review: No marks deducted |
| Total Marks | 100 Marks |
JEE Main Mathematics Chapter-Wise Weightage
The most important sections in the JEE Main Mathematic are Calculus and Algebra. These topics carry approximately 35 to 40% weightage in the exam.
The detailed chapter-wise weightage for mathematics is given in the table below for classes 11th and 12th.
Class 11 Mathematics High-weightage Topics:
| Chapter | Approximate Weightage |
|---|---|
| Sets, Relations & Functions | 3.3% |
| Complex Numbers & Quadratic Equations | 3.3% |
| Permutations & Combinations | 3.3% |
| Binomial Theorem | 3.3% |
| Sequences & Series | 6.6% |
| Straight Lines | 6.6% |
| Conic Sections (Parabola, Ellipse, Hyperbola) | 9.9% |
| Trigonometric Equations | 3.3% |
Mathematics Chapter-wise Weightage for Class 12 Topics:
| Chapter | Approximate Weightage |
|---|---|
| Matrices & Determinants | 6.6% |
| Limits, Continuity & Differentiability | 3.3% |
| Integral Calculus (Definite & Indefinite Integrals) | 6.6% |
| Differential Equations | 3.3% |
| Vector Algebra | 3.3% |
| Three-Dimensional Geometry | 6.6% |
| Probability & Statistics | 6.6% |
JEE Main Last 5 Year Mathematics Papers Pdf
You can download the JEE Main last 5 years’ Mathematics pdf with solutions from the table given below:
JEE Main 2024 Mathematics Question Paper Session 1
| Exam Date | Question Paper | Solution PDF |
|---|---|---|
| JEE Main 2024 Feb 1 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Feb 1 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 31 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 31 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 30 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 30 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 29 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 29 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 27 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 Jan 27 Shift 1 Mathematics Question Paper | Download | Check Solution |
JEE Main 2024 Mathematics Question Paper Session 2
| Exam Date and Shift | Question Paper | Solution PDF |
|---|---|---|
| JEE Main 2024 April 4 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 4 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 5 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 5 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 6 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 6 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 8 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 8 Shift 2 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 9 Shift 1 Mathematics Question Paper | Download | Check Solution |
| JEE Main 2024 April 9 Shift 2 Mathematics Question Paper | Download | Check Solution |
JEE Main 2023 Mathematics Question Paper
| Exam Date | Mathematics Question Paper PDF |
|---|---|
| Mathematics 6 April Shift 1 Question Paper | Check Here |
| Mathematics 6 April Shift 2 Question Paper | Check Here |
| Mathematics 8 April Shift 1 Question Paper | Check Here |
| Mathematics 8 April Shift 2 Question Paper | Check Here |
| Mathematics 10 April Shift 1 Question Paper | Check Here |
| Mathematics 10 April Shift 2 Question Paper | Check Here |
| Mathematics 11 April Shift 1 Question Paper | Check Here |
| Mathematics 11 April Shift 2 Question Paper | Check Here |
| Mathematics 12 April Shift 1 Question Paper | Check Here |
| Mathematics 13 April Shift 1 Question Paper | Check Here |
| Mathematics 13 April Shift 2 Question Paper | Check Here |
| Mathematics 15 April Shift 1 Question Paper | Check Here |
JEE Main 2023 Mathematics Question Paper Session 1
| Exam Date and Shift | Mathematics Question Paper PDF |
|---|---|
| Mathematics 24 January Shift 1 Question Paper | Check Here |
| Mathematics 24 January Shift 2 Question Paper | Check Here |
| Mathematics 25 January Shift 1 Question Paper | Check Here |
| Mathematics 25 January Shift 2 Question Paper | Check Here |
| Mathematics 29 January Shift 1 Question Paper | Check Here |
| Mathematics 29 January Shift 2 Question Paper | Check Here |
| Mathematics 30 January Shift 1 Question Paper | Check Here |
| Mathematics 30 January Shift 2 Question Paper | Check Here |
| Mathematics 31 January Shift 1 Question Paper | Check Here |
| Mathematics 31 January Shift 2 Question Paper | Check Here |
| Mathematics 1 February Shift 1 Question Paper | Check Here |
| Mathematics 1 February Shift 2 Question Paper | Check Here |
JEE Main 2022 Mathematics Question Paper with Solution PDF
| Exam Date | Shift/ Slot | Question Paper PDF |
|---|---|---|
| July 25 | Shift 1 | Check Here |
| July 25 | Shift 2 | Check Here |
| July 26 | Shift 1 | Check Here |
| July 26 | Shift 2 | Check Here |
| July 27 | Shift 1 | Check Here |
| July 27 | Shift 2 | Check Here |
| July 28 | Shift 1 | Check Here |
| July 28 | Shift 2 | Check Here |
| July 29 | Shift 1 | Check Here |
| July 29 | Shift 2 | Check Here |
JEE Main 2022 Mathematics Question Paper with Solution PDF- Phase 1
| Exam Date | Shift/ Slot | Question Paper PDF |
|---|---|---|
| June 29 | Shift 1 | Check Here |
| June 29 | Shift 2 | Check Here |
| June 28 | Shift 1 | Check Here |
| June 28 | Shift 2 | Check Here |
| June 27 | Shift 1 | Check Here |
| June 27 | Shift 2 | Check Here |
| June 26 | Shift 1 | Check Here |
| June 26 | Shift 2 | Check Here |
| June 25 | Shift 1 | Check Here |
| June 25 | Shift 2 | Check Here |
| June 24 | Shift 1 | Check Here |
| June 24 | Shift 2 | Check Here |
JEE Main 2021 Mathematics Question Paper- Download PDF
JEE Main 2021 Mathematics Question Paper with Solution (Session 4- August)- Download PDF
| Exam Date | Shift/ Slot | Question Paper PDF |
|---|---|---|
| August 26 | Shift 1 | Check Here |
| August 26 | Shift 2 | Check Here |
| August 27 | Shift 1 | Check Here |
| August 27 | Shift 2 | Check Here |
| August 31 | Shift 1 | Check Here |
| August 31 | Shift 2 | Check Here |
| September 1 | Shift 2 | Check Here |
JEE Main 2021 Mathematics Question Paper with Solution (Session3- July)- Download PDF
| Exam Date | Shift/ Slot | JEE Main Question Paper PDF |
|---|---|---|
| July 22 | Shift 2 | Check Here |
| July 25 | Shift 1 | Check Here |
| July 25 | Shift 2 | Check Here |
| July 27 | Shift 1 | Check Here |
| August 3 | Shift 1 | Check Here |
| August 3 | Shift 2 | Check Here |
| August 4 | Shift 1 | Check Here |
| August 4 | Shift 2 | Check Here |
JEE Main 2021 Mathematics Question Paper with Solution (Session 2- March)- Download PDF
| Exam Date | Shift/ Slot | Question Paper PDF |
|---|---|---|
| March 16 | Shift 1 | Check Here |
| March 16 | Shift 2 | Check Here |
| March 17 | Shift 1 | Check Here |
| March 17 | Shift 2 | Check Here |
| March 18 | Shift 1 | Check Here |
| March 18 | Shift 2 | Check Here |
JEE Main 2021 Mathematics Question Paper with Solution (Session 1- February)- Download PDF
| Exam Date | Shift/ Slot | Question Paper PDF |
|---|---|---|
| February 24 | Shift 1 | Check Here |
| February 24 | Shift 2 | Check Here |
| February 25 | Shift 1 | Check Here |
| February 25 | Shift 2 | Check Here |
| February 26 | Shift 1 | Check Here |
| February 26 | Shift 2 | Check Here |
JEE Main 2020 Mathematics Question Paper with Solutions- Download PDF
JEE Main 2020 Mathematics Question Paper with Solutions (Session 2- September)- Download PDF
| Exam Date | Shift/ Slot | Question Paper PDF |
|---|---|---|
| September 2 | Shift 1 | Check Here |
| September 2 | Shift 2 | Check Here |
| September 3 | Shift 1 | Check Here |
| September 3 | Shift 2 | Check Here |
| September 4 | Shift 1 | Check Here |
| September 4 | Shift 2 | Check Here |
| September 5 | Shift 1 | Check Here |
| September 5 | Shift 2 | Check Here |
| September 6 | Shift 1 | Check Here |
| September 6 | Shift 2 | Check Here |
JEE Main 2020 Mathematics Question Paper with Solutions (Session 1- January)- Download PDF
| Exam Date | Shift/ Slot | JEE Main Question Paper PDF |
| January 8 | Shift 1 | Check Here |
| January 8 | Shift 2 | Check Here |
| January 9 | Shift 1 | Check Here |
| January 9 | Shift 2 | Check Here |
Important Books for Mathematics:
Frequently Asked Questions
What is the purpose of integral calculus?
The main purpose of integral calculus is to calculate quantities that are affected by continuous change. It is used to find areas, volumes of irregular shapes, displacement quantities, and velocity.
Integral calculus is also used in Physics as well as Economics to solve complex data based problem. It is used to measure accumulation and predict outcomes across Engineering and Mathematics
What is the real-world application of calculus?
Calculus is widely used for real-life purposes and it helps solve problems related to change, motion, and optimization. Some fields where calculus is mostly used are:
- Physics and Engineering: Calculus is used to analyze motion, force, and energy in these fields. Engineers use calculus to design bridges, building,s, and mechanical systems.
- Medicine and Biology: In medicine and biology calculus helps in tracking the growth of tumors, the spread of diseases, and blood flow dynamics.
- Economics and Finance: Calculating profit maximization, cost minimization, and analyzing market trends can be done with the help of integral calculus.
Is Integral Calculus Used in Physics?
Yes, integral calculus is used in physics to solve problems related to motion, forces, and energy. It is mainly used in branches like mechanics, electromagnetism, and thermodynamics. Some of the concepts of Integral calculus used in physics are:
- Kinematics
- Work and Energy
- Electricity and Magnetism
- Fluid Dynamics
Who is the father of calculus?
Issac Newton and Gottfried Wilhelm are both credited as founders of calculus. Newton developed calculus to explain motion and changing values, Leibniz introduced the symbols and rules that are used commonly today, like the integral (∫) and differential (d) signs.
Both of them have worked in creating calculus, which is why both of them are considered as father of calculus.
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