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Chapter 7 Class 12 Integrals

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Get NCERT Solutions of Class 12 Integration, Chapter 7 of the NCERT book. Solutions of all questions, examples and supplementary questions explained here. Download formulas and practice questions as well.

 

Topics include

  • Integration as anti-derivative - Basic definition of integration. Using derivative rules, finding integration
  • Integration using Trigonometry Formulas - where we use trigonometry formulas like cos 2x, sin2 x, sin 3x, Inverse formulas and make the function easier to integrate
  • Integration by substitution - Where we substitute functions as some other functions and integrate using the formulas we know - xn, lnx, ex to find the integration
  • Integration by parts - We do integration by using by parts formula
  • By parts integration of ex - We use integration formula of ex (f(x) + f'(x)) to solve questions
  • Integration by partial fractions - We use partial fractions to solve the integration. Like in this question.
  • Integration by special formulas - We use special formulas mentioned in our Integral Table to solve questions
  • Integration as limit as a sum - We use basic definition of integration , Integration = Area to form limit as a sum formula and then solve its questions
  • Definite Integration - Solving definite integration using methods of indefinite integration, and using properties of definite integration

 

To check all formulas of Integrals used in this chapter, check Integration Formulas

Important Questions are marked as Important, you can also check all Important Questions for Class 12 Maths. As well as Sample papers.

Serial order wise

  Ex 7.1
  Ex 7.2
  Ex 7.3
  Ex 7.4
  Ex 7.5
  Ex 7.6
  Ex 7.7
  Ex 7.8
  Ex 7.9
  Ex 7.10
  Examples
  Miscellaneous
  Case Based Questions (MCQ)
  NCERT Exemplar MCQ
  Area as a sum

Concept wise

  Using Formulaes
  Using Trignometric Formulaes
  Integration by substitution - x^n
  Integration by substitution - lnx
  Integration by substitution - e^x
  Integration by substitution - Trignometric - Normal
  Integration by substitution - Trignometric - Inverse
  Integration using trigo identities - sin^2,cos^2 etc formulae
  Integration using trigo identities - a-b formulae
  Integration using trigo identities - 2x formulae
  Integration using trigo identities - 3x formulae
  Integration using trigo identities - CD and CD inv formulae
  Integration using trigo identities - Inv Trigo formulae
  Integration by parts
  Integration by parts - e^x integration
  Integration by specific formulaes - Formula 1
  Integration by specific formulaes - Formula 2
  Integration by specific formulaes - Formula 3
  Integration by specific formulaes - Formula 4
  Integration by specific formulaes - Formula 5
  Integration by specific formulaes - Formula 6
  Integration by specific formulaes - Formula 7
  Integration by specific formulaes - Formula 8
  Integration by specific formulaes - Method 9
  Integration by specific formulaes - Method 10
  Integration by partial fraction - Type 1
  Integration by partial fraction - Type 2
  Integration by partial fraction - Type 3
  Integration by partial fraction - Type 4
  Integration by partial fraction - Type 5
  Definite Integral as a limit of a sum
  Definite Integration - By Formulae
  Definite Integration - By Partial Fraction
  Definite Integration - By e formula
  Definite Integration - By Substitution
  Definite Integration by properties - P2
  Definite Integration by properties - P3
  Definite Integration by properties - P4
  Definite Integration by properties - P6
  Definite Integration by properties - P7

What's in it?

Get NCERT Solutions of Class 12 Integration, Chapter 7 of the NCERT book. Solutions of all questions, examples and supplementary questions explained here. Download formulas and practice questions as well.

 

Topics include

  • Integration as anti-derivative - Basic definition of integration. Using derivative rules, finding integration
  • Integration using Trigonometry Formulas - where we use trigonometry formulas like cos 2x, sin2 x, sin 3x, Inverse formulas and make the function easier to integrate
  • Integration by substitution - Where we substitute functions as some other functions and integrate using the formulas we know - xn, lnx, ex to find the integration
  • Integration by parts - We do integration by using by parts formula
  • By parts integration of ex - We use integration formula of ex (f(x) + f'(x)) to solve questions
  • Integration by partial fractions - We use partial fractions to solve the integration. Like in this question.
  • Integration by special formulas - We use special formulas mentioned in our Integral Table to solve questions
  • Integration as limit as a sum - We use basic definition of integration , Integration = Area to form limit as a sum formula and then solve its questions
  • Definite Integration - Solving definite integration using methods of indefinite integration, and using properties of definite integration

 

To check all formulas of Integrals used in this chapter, check Integration Formulas

Important Questions are marked as Important, you can also check all Important Questions for Class 12 Maths. As well as Sample papers.