Definite Integrals
Kerala Board · Class 12 · Mathematics
Complete topic list for Definite Integrals in Kerala Board Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.
Topics in Definite Integrals
Definition and Geometric Interpretation
- Definite integral as limit of sum: ∫[a to b] f(x)dx = lim(n→∞) h[f(a) + f(a+h) + ... + f(a+(n-1)h)] where h = (b-a)/n
- Represents area under curve y = f(x) from x = a to x = b
- Upper limit 'b' and lower limit 'a' are fixed values
Properties of Definite Integrals
- Property 1: ∫[a to b] f(x)dx = -∫[b to a] f(x)dx (reversing limits changes sign)
- Property 2: ∫[a to c] f(x)dx = ∫[a to b] f(x)dx + ∫[b to c] f(x)dx (additive property)
- Property 3: ∫[a to b] f(x)dx = ∫[a to b] f(a+b-x)dx (substitution property)
Evaluation by Substitution Method
- Step 1: Choose appropriate substitution u = g(x)
- Step 2: Find du = g'(x)dx
- Step 3: Change limits: when x = a, u = g(a); when x = b, u = g(b)
Applications - Area Under Curves
- Area under y = f(x) from x = a to x = b: A = ∫[a to b] f(x)dx (when f(x) ≥ 0)
- Area between two curves: A = ∫[a to b] |f(x) - g(x)|dx
- When f(x) > g(x): A = ∫[a to b] [f(x) - g(x)]dx
Key Concepts
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What are the important topics in Definite Integrals for Kerala Board Class 12 Mathematics?
Definite Integrals covers several key topics that are frequently asked in Kerala 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 Integrals — Kerala Board Class 12 Mathematics?
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
- Kerala Board of Public Examinations — keralapareekshabhavan.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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