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

Definite Integrals

Telangana Board · Class 12 · Mathematics

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

43 questions20 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 Board Class 12 Mathematics

Topics in Definite Integrals

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

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.

More resources for Definite Integrals

All 31 chapters — Telangana Board 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 Board Class 12 Mathematics.

Try Super Tutor Free
Try the full chapter — Free