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Definite Integration

Maharashtra Board · Class 12 · Mathematics & Statistics - Science

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

45 questions20 flashcards5 concepts

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Key Topics to Revise

1

Fundamental Theorem of Integral Calculus

  • If f(x) is continuous on [a,b] and F(x) is an antiderivative of f(x), then ∫ₐᵇ f(x)dx = F(b) - F(a)
  • The constant of integration cancels out in definite integrals
  • Notation: ∫ₐᵇ f(x)dx = [F(x)]ₐᵇ where 'a' is lower limit and 'b' is upper limit
2

Standard Integration Techniques for Definite Integrals

  • Apply integration by parts: ∫udv = [uv]ₐᵇ - ∫vdu evaluated from a to b
  • Use substitution method with appropriate limit changes
  • Apply partial fraction decomposition for rational functions
3

Properties of Definite Integrals

  • Property 1: ∫ₐᵃ f(x)dx = 0 (integral from a point to itself is zero)
  • Property 2: ∫ₐᵇ f(x)dx = -∫ᵇₐ f(x)dx (reversing limits changes sign)
  • Property 3: ∫ₐᵇ f(x)dx = ∫ₐᶜ f(x)dx + ∫ᶜᵇ f(x)dx (additivity property)
4

Advanced Problem-Solving Techniques

  • Parametric evaluation: Find unknown parameters using given integral values
  • Comparison method: Compare integrals to establish inequalities or equalities
  • Splitting integrals at points of discontinuity or where integrand changes form

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Full Notes

Key Concepts

If f(x) is continuous on [aFor a continuous function f(x) onFor symmetric intervals [∫ₐᵇ f(x)dx = ∫ₐᵇ f(a+b∫ₐᵇ u dv = [uv]ₐᵇ

Frequently Asked Questions

What are the important topics in Definite Integration for Maharashtra Board Class 12 Mathematics & Statistics - Science?
Definite 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 Definite 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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