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Integration and its Applications

CBSE · Class 12 · Applied Mathematics

Complete topic list for Integration and its Applications in CBSE Class 12 Applied Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

45 questions25 flashcards5 concepts

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4 Topics · CBSE Class 12 Applied Mathematics

Topics in Integration and its Applications

1

Indefinite Integration - Basic Concepts

  • Integration is the inverse process of differentiation
  • If d/dx[F(x)] = f(x), then ∫f(x)dx = F(x) + C
  • The constant C is called the constant of integration
2

Integration by Substitution

  • Used when direct integration is not possible
  • Rule: ∫f(g(x))g'(x)dx = ∫f(t)dt, where g(x) = t
  • Choose substitution that simplifies the integrand
3

Integration by Partial Fractions

  • Used for rational functions P(x)/Q(x) where degree of P(x) < degree of Q(x)
  • If improper (degree P(x) ≥ degree Q(x)), first divide using long division
  • Decompose into simpler fractions based on factors of denominator
4

Integration by Parts

  • Used for integrating product of two functions
  • Formula: ∫uv' dx = uv - ∫u'v dx
  • Choose u and v' using ILATE rule (Inverse trig, Log, Algebraic, Trig, Exponential)

Key Concepts

If d(F(x))/dx = f(x)Key formulae includeMethod where we substitute a partTechnique for integrating rational functions P(x)/Q(x)Used for integrating products of functions

Frequently Asked Questions

What are the important topics in Integration and its Applications for CBSE Class 12 Applied Mathematics?
Integration and its Applications covers several key topics that are frequently asked in CBSE Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Integration and its Applications — CBSE Class 12 Applied Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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