CBSE · Class 12 · Mathematics · Chapter 7

Integrals

Indefinite and definite integration.

9 lessons 140 min
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Lessons in this chapter

  1. 1Antiderivatives and Indefinite IntegralsRecover functions from their rates of change and build a reliable first toolkit for integration.
  2. 2Integration by SubstitutionTurn composite integrands into familiar forms by changing the variable carefully.
  3. 3Integrating with Trigonometric IdentitiesUse identities to reveal standard integrals hidden inside trigonometric powers, products, and quotients.
  4. 4Standard Integrals Involving Quadratic ExpressionsRecognise six useful standard forms and transform general quadratic expressions into them.
  5. 5Integration by Partial FractionsBreak rational functions into simpler pieces that integrate through familiar rules.
  6. 6Integration by Parts and Radical FormsReverse the product rule, then use it to derive integrals containing logarithms, inverse functions, and square roots.
  7. 7Definite Integrals and the Fundamental TheoremConnect accumulated area to antiderivatives and evaluate definite integrals with the correct limits.
  8. 8Properties and Symmetry of Definite IntegralsUse interval structure, reflection, and parity to simplify definite integrals before calculating.
  9. 9Chapter Summary and PracticeConnect every integration method and choose a justified route through mixed chapter problems.
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