Integral Calculus is one of the most important topics for both JEE Mains 2025 and JEE Advanced 2025 Mathematics. It plays a significant role in solving complex problems and holds substantial weight in the exam. Of the total syllabus Integral Calculus holds 35 to 40 % weightage in JEE Advanced and 25% in JEE Mains. Due to this heavy weightage, Integral calculus is very essential for maximizing scores in both of these exams.
In this guide, we will cover the most important concepts, formulas, and problem-solving techniques to help you ace Integral Calculus in JEE Mains 2025
Why Integral Calculus is Important for JEE Mains 2025
Integral Calculus is an essential part of the JEE Mains Mathematics syllabus. It covers various applications, including finding areas, solving differential equations, and determining functions from their derivatives.
Weightage of Integral Calculus in JEE Mains and JEE Advanced
Differentiation in Integral Calculus contributes around 5 to 6 questions in the JEE Mains mathematics section and 6 to 8 Questions in JEE Advanced 2025 mathematics. The most common topics that Integral Calculus include:
- Indefinite Integrals (Basic Integration techniques)
- Functions (High-Weightage Chapters)
- Definite Integrals (Properties and Applications)
- Area Under Curves
- Differential Equations
A strong hold over these topics can significantly improve a candidate’s JEE Mains 2025 rank.
Also Check:
Topics Covered in Integral Calculus for JEE Mains 2025
Indefinite Integrals
Indefinite integration involves finding the antiderivative of a function. It is represented as: ∫f(x)dx=F(x)+C
Where C is the constant of integration.
Definite Integrals
Definite integration is used to find the exact value of an integral over a given interval: ∫ab f(x)dx
This topic is one of the high-weightage topics for JEE Mains 2025, especially in physics-related problems.
Area Under Curves
One of the most important applications of integrals is finding the area enclosed between curves. This is useful in real-world physics problems and engineering applications.
Differential Equations
Differential equations are used to model dynamic systems in physics and engineering. JEE Mains focuses on first-order and first-degree differential equations and their solutions.
Read: JEE Main 2025: 24-Hour Strategy to Score 99 percentile
Calculus Chapter Weightage for JEE Mains
In JEE Main 2025 Calculus syllabus functions have the maximum weightage while Differentiation is the less weightage topic in calculus. Details related to calculus weightage is described below:
| Topic Name | Total Number of Questions (Expected) |
|---|---|
| Differentiation | 6 |
| Continuity and Differentiability | 8 |
| Limits | 9 |
| Indefinite Integration | 14 |
| Application of Derivatives | 20 |
| Differential Equations | 24 |
| Sets and Relations | 34 |
| Definite Integration | 32 |
| Area Under Curves | 32 |
| Functions | 38 |
JEE Main 2025 and JEE Advance 2025: Preparation Strategy for Integral Calculus
Build Your Basics
Start by understanding the fundamental concepts of integration.
Learn how integration is the reverse of differentiation.
Practice basic integral formulas and their derivations.
Memorize Standard Integration Formulas
Some frequently used Integral Calculus formulas include:
- ∫ xn dx = x(n + 1)/(n + 1)+ C
- ∫ 1 dx = x + C
- ∫ ex dx = ex + C
- ∫ 1/x dx = log |x| + C
- ∫ ax dx = ax /log a+ C
- ∫ ex [f(x) + f'(x)] dx = ex f(x) + C
Memorizing these formulas will help candidates solve problems quickly in the JEE Mains 2025 exam.
Master Definite Integrals and Their Applications
- Learn and apply properties of definite integrals, such as ∫ab f(x)dx=∫ab f(a+b−x)dx
- Understand how definite integrals relate to area calculations.
- Solve previous years’ JEE Mains questions on this topic.
Practice Area Under Curves
- Learn how to set up integrals to calculate areas.
- Understand the concept of bounded regions and how to evaluate their areas using integration.
Solve Differential Equations
- Understand the formation and solution of differential equations.
- Learn variable separable methods and homogeneous differential equations.
- Solve NCERT and JEE Mains-level problems to strengthen your concepts.
Practice and Revision Tips
- Practicing past JEE Mains questions helps in understanding the exam pattern.
- Attempt mock tests regularly to improve time management and accuracy.
- Analyze mistakes and work on weaker areas.
Recommended Books for Integral Calculus Preparation
To master Integral Calculus, refer to these best books for JEE Mains 2025:
- I.A. Maron – Problems in Calculus of One Variable
- R.D. Sharma – Mathematics for JEE
- Cengage Mathematics – Integral Calculus
These books provide a strong conceptual foundation and contain JEE-level problems for practice.
Conclusion
Integral Calculus is a crucial part of JEE Mains 2025 mathematics, and mastering it requires conceptual clarity, practice, and problem-solving skills.
- Focus on basic concepts, formulas, and their applications.
- Practice previous year's questions and mock tests regularly.
- Refer to standard books and expert resources for in-depth understanding.
By following this structured study plan, candidate can strengthen their grip on Integral Calculus and increase their JEE Mains 2025 score.
Frequently Asked Questions
Name some important topics in Integral Calculus for JEE Mains 2025.
The important topics for Integral calculus include Indefinite Integrals, Definite Integrals, Area Under Curves, and Differential Equations.
How can a candidate improve his/her problem-solving speed in Integral Calculus?
Regular practice, solving previous years’ questions, and taking mock tests will help improve speed.
Are Definite Integrals Difficult in JEE Mains 2025?
Definite Integrals can be tricky, but with strong conceptual understanding and regular practice, they can be mastered easily.
Which books should a candidate refer to for preparing Integral Calculus for JEE Mains?
Some of the best books include I.A. Maron, R.D. Sharma, and Cengage Mathematics for comprehensive preparation.
