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Integration and its Applications — Revision Notes

CBSE · Class 12 · Applied Mathematics

Integration and its Applications revision notes for CBSE Class 12 Applied Mathematics: 4 topics in quick points.

42 questions25 flashcards8 formulas & key relations5 concepts

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Key Topics to Revise

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)

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Full Notes

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?
Key topics in Integration and its Applications include Indefinite Integration - Basic Concepts, Integration by Substitution, Integration by Partial Fractions, Integration by Parts. Study these first, then practise questions on each for the CBSE Class 12 board exam.
How should I revise Integration and its Applications for the CBSE Class 12 board exam?
Learn the core ideas first, then work through the 42 practice questions on Integration and its Applications. Revise 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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All CBSE Class 12 Applied Mathematics Revision Notes

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