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Revision Notes
Definite Integration — Revision Notes
JEE Mains · Mathematics
Free Definite Integration revision notes for JEE Mains Mathematics 2026 — key concepts, formulas, and definitions for quick revision.
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![A graph illustrating the concept of a definite integral as the net signed area between a curve f(x) and the x-axis over a closed interval [a, b]. Areas above the x-axis are positive, and areas below a](https://s3.ap-southeast-2.amazonaws.com/super-tutor/production/educational-images/mathematics/calculus_definite_integration_area_under_curve_labeled_diagram.png "Definite Integral as Net Signed Area")
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Key concepts, formulas, and definitions from Definite Integration for JEE Mains Mathematics preparation.
Key Topics to Revise
1
Definite Integration as Limit of Sum
- Definite integral represents area under curve y = f(x) between x = a and x = b
- ∫[a to b] f(x)dx = lim[n→∞] h∑[r=0 to n-1] f(a + rh) where h = (b-a)/n
- Can be calculated using upper sum or lower sum - both give same result
2
Fundamental Theorems of Integral Calculus
- First Fundamental Theorem: If F(x) = ∫[a to x] f(t)dt, then F'(x) = f(x)
- Second Fundamental Theorem: ∫[a to b] f(x)dx = F(b) - F(a) where F'(x) = f(x)
- Area function F(x) represents area from fixed point to variable point
3
Properties of Definite Integration
- ∫[a to b] f(x)dx = -∫[b to a] f(x)dx (reversing limits changes sign)
- ∫[a to b] f(x)dx = ∫[a to c] f(x)dx + ∫[c to b] f(x)dx (splitting limits)
- ∫[a to b] f(x)dx = ∫[a to b] f(a+b-x)dx (substitution property)
4
Integration by Parts for Definite Integrals
- ∫[a to b] u dv = [uv]ₐᵇ - ∫[a to b] v du
- Choose u using ILATE rule (Inverse, Logarithmic, Algebraic, Trigonometric, Exponential)
- Often used for products of different types of functions
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Key Concepts
For a continuous function f(x) onFirst Fundamental TheoremKey properties includeWhen substituting u = g(x)Formula
Frequently Asked Questions
What topics are covered in Definite Integration for JEE Mains?
Definite Integration is an important chapter in JEE Mains Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Definite Integration as Limit of Sum, Fundamental Theorems of Integral Calculus, Properties of Definite Integration, Integration by Parts for Definite Integrals.
How important is Definite Integration for JEE Mains?
Definite Integration is a frequently tested chapter in JEE Mains Mathematics. Questions from this chapter appear regularly in previous year papers. There are 90 practice questions available for this chapter.
How to prepare Definite Integration for JEE Mains?
Start by understanding the core concepts, then solve practice questions. Focus on formulas and their applications. Use revision notes for quick review before the exam.
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