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Revision Notes

Definite Integrals

Telangana Open School (TOSS) · Class 12 · Mathematics

Quick revision notes for Definite Integrals — Telangana Open School (TOSS) Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

45 questions25 flashcards5 concepts

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Key Topics to Revise

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.

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Full Notes

Key Concepts

The definite integral ∫ₐᵇ f(x)dxIf f(x) is continuous on [aKey properties includeThe definite integral ∫ₐᵇ f(x)dx givesFor integrals like ∫₀^{π/2} sinⁿx dx

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.

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