Chapter 13 of 27
Important Topics
Integrals — Important Topics
CUSAT CAT · Mathematics
Most important topics from Integrals for CUSAT CAT Mathematics 2026 — high-weightage areas based on previous year analysis.
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Get startedIntegrals — Syllabus & Topics
Topics covered in Integrals for CUSAT CAT Mathematics.
Topics in Integrals
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
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 CUSAT CAT?
Integrals is an important chapter in CUSAT CAT 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 CUSAT CAT?
Integrals is a frequently tested chapter in CUSAT CAT 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 CUSAT CAT?
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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