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Integration

Maharashtra Board · Class 12 · Mathematics & Statistics - Science

Quick revision notes for Integration — Maharashtra Board Class 12 Mathematics & Statistics - Science. Key concepts, formulas, and definitions for last-minute revision.

45 questions22 flashcards5 concepts

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Key Topics to Revise

1

Basic Integration and Standard Forms

  • Integration is the inverse operation of differentiation
  • The constant of integration (c) must always be included in indefinite integrals
  • Linear combination rule: ∫[af(x) + bg(x)]dx = a∫f(x)dx + b∫g(x)dx
2

Method of Substitution

  • Used when integrand is in the form f[g(x)]·g'(x)
  • Choose substitution u = g(x), then du = g'(x)dx
  • Transform entire integral in terms of new variable
3

Special Integration Techniques

  • Integration of expressions involving √(x² ± a²)
  • Integration of rational functions with specific forms
  • Use standard results for quick evaluation
4

Integration by Parts

  • Used for products of two different types of functions
  • Formula: ∫u·v dx = u∫v dx - ∫(du/dx·∫v dx)dx
  • Choose u using ILATE rule (Inverse trig, Logarithmic, Algebraic, Trigonometric, Exponential)

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Full Notes

Key Concepts

If f(x) and g(x) are functionsKey formulas includeWhen dealing with composite functionsFor products of functionsFor rational functions P(x)/Q(x) where degree

Frequently Asked Questions

What are the important topics in Integration for Maharashtra Board Class 12 Mathematics & Statistics - Science?
Integration covers several key topics that are frequently asked in Maharashtra Board 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 — Maharashtra Board Class 12 Mathematics & Statistics - Science?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision 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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