Integration
Maharashtra Board · Class 12 · Mathematics & Statistics
Quick revision notes for Integration — Maharashtra Board Class 12 Mathematics & Statistics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
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
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
Special Integration Techniques
- Integration of expressions involving √(x² ± a²)
- Integration of rational functions with specific forms
- Use standard results for quick evaluation
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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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.
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