Chapter 13 of 27
Revision Notes
Integrals — Revision Notes
MHT-CET · Mathematics
Free Integrals revision notes for MHT-CET Mathematics 2026 — key concepts, formulas, and definitions for quick revision.
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Key concepts, formulas, and definitions from Integrals for MHT-CET Mathematics preparation.
Key Topics to Revise
1
Basic Integration Rules and Standard Forms
- Integration is the inverse of differentiation - if d/dx[F(x)] = f(x), then ∫f(x)dx = F(x) + C
- The constant of integration C is essential in indefinite integrals
- Learn all standard integral formulas by heart as they form the foundation
2
Integration by Substitution Method
- Used when integrand is in the form f(g(x)) × g'(x) or can be transformed into this form
- Choose substitution u = g(x), then du = g'(x)dx
- Three main types: direct substitution, trigonometric substitution, and algebraic substitution
3
Integration by Parts
- Used for products of two different types of functions using formula ∫udv = uv - ∫vdu
- ILATE rule for choosing u: Inverse functions, Logarithmic, Algebraic, Trigonometric, Exponential
- Sometimes requires applying integration by parts twice (for functions like e^x sin x)
4
Integration of Rational Functions by Partial Fractions
- Used when integrand is a proper rational function (degree of numerator < degree of denominator)
- If improper, first divide to get polynomial + proper rational function
- Four cases based on factors of denominator: linear non-repeated, linear repeated, quadratic non-repeated, quadratic repeated
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Key Concepts
If F'(x) = f(x)Essential formulas includeWhen integrating composite functionsFor products of functionsFor rational functions P(x)/Q(x) where degree
Frequently Asked Questions
What topics are covered in Integrals for MHT-CET?
Integrals is an important chapter in MHT-CET Mathematics. It covers key concepts and formulas that are frequently tested in the exam. Key topics include: Basic Integration Rules and Standard Forms, Integration by Substitution Method, Integration by Parts, Integration of Rational Functions by Partial Fractions.
How important is Integrals for MHT-CET?
Integrals is a frequently tested chapter in MHT-CET Mathematics. Questions from this chapter appear regularly in previous year papers. There are 750 practice questions available for this chapter.
How to prepare Integrals for MHT-CET?
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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