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Revision Notes

Definite Integrals — Revision Notes

Telangana Open School (TOSS) · Class 12 · Mathematics

Definite Integrals revision notes for Telangana Open School (TOSS) Class 12 Mathematics: 4 topics in quick points.

45 questions25 flashcards14 formulas & key relations5 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?
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 Revision Notes

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