Integration and its Applications
CBSE · Class 12 · Applied Mathematics
Quick revision notes for Integration and its Applications — CBSE Class 12 Applied Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
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
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
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
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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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.
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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