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Revision Notes

Definite Integrals

Telangana Board · Class 12 · Mathematics

Quick revision notes for Definite Integrals — Telangana Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

43 questions20 flashcards5 concepts

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Key Topics to Revise

1

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
2

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)
3

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)
4

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

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Full Notes

Key Concepts

For a continuous function f(x) onIf F(x) is an antiderivativeSeven key properties that simplify evaluationWhen using substitution u = g(x)Three main types

Frequently Asked Questions

What are the important topics in Definite Integrals for Telangana Board Class 12 Mathematics?
Definite Integrals covers several key topics that are frequently asked in Telangana 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 — Telangana 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

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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