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Syllabus

Definite Integrals — Syllabus

Telangana Open School (TOSS) · Class 12 · Mathematics

What Definite Integrals covers in Telangana Open School (TOSS) Class 12 Mathematics: 4 topics, for the 2026-27 session.

45 questions25 flashcards14 formulas & key relations5 concepts

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4 Topics · Telangana Open School (TOSS) Class 12 Mathematics · 2026-27

Topics in Definite Integrals

1

Definite Integral as Limit of Sum

  • The definite integral ∫ₐᵇ f(x) dx is defined as the limit of a sum of areas of rectangles under the curve.
  • Divide the interval [a, b] into n equal parts, each of width h = (b−a)/n.
  • Use left or right endpoints to evaluate function values: f(a), f(a+h), ..., f(a+(n−1)h).
2

Fundamental Theorem of Calculus

  • If F(x) is an antiderivative of f(x), then ∫ₐᵇ f(x) dx = F(b) − F(a).
  • This theorem connects differentiation and integration.
  • It allows us to evaluate definite integrals without using limits of sums.
3

Properties of Definite Integrals

  • ∫ₐᵇ f(x) dx = −∫ᵇₐ f(x) dx
  • ∫ₐᵇ f(x) dx = ∫ₐᶜ f(x) dx + ∫ᶜᵇ f(x) dx for a < c < b
  • ∫₀ᵃ f(x) dx = ∫₀ᵃ f(a−x) dx
4

Integration by Substitution

  • Substitute a new variable to simplify the integrand.
  • Change the limits of integration according to the substitution.
  • Integrate with respect to the new variable and evaluate directly.

Key Concepts

Central concept: Definite Integrals

Definition as Limit of SumFundamental Theorem of CalculusProperties of Definite IntegralsEvaluation by SubstitutionApplications in Area CalculationReduction Formulae

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Frequently Asked Questions

What are the important topics in Definite Integrals for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Definite Integrals include Definite Integral as Limit of Sum, Fundamental Theorem of Calculus, Properties of Definite Integrals, Integration by Substitution. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Definite Integrals for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Definite Integrals. Revise definitions regularly and use flashcards for quick recall 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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All Telangana Open School (TOSS) Class 12 Mathematics Syllabus

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