Skip to main content
Super TutorResources
Chapter 24 of 31
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Syllabus

Definite Integrals

Telangana Open School (TOSS) · Class 12 · Mathematics

Complete topic list for Definite Integrals in Telangana Open School (TOSS) Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

45 questions25 flashcards5 concepts

Interactive on Super Tutor

Studying Definite Integrals? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for syllabus and more.

Try Super Tutor — Free

1,000+ Class 12 students started this chapter today

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

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

Frequently Asked Questions

What are the important topics in Definite Integrals for Telangana Open School (TOSS) Class 12 Mathematics?
Definite Integrals covers several key topics that are frequently asked in Telangana Open School (TOSS) 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 Open School (TOSS) Class 12 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and 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.

More resources for Definite Integrals

All 31 chapters — Telangana Open School (TOSS) Class 12 Mathematics Syllabus

For serious students

Get the full Definite Integrals chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for Telangana Open School (TOSS) Class 12 Mathematics.

Try Super Tutor Free
Try the full chapter — Free