Class 12

Chapter 7 Class 12 Integrals

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 
Ex 7.11 
Examples 
Miscellaneous 

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 
Definate Integral as a limit of a sum 
Definate Integration - By Formulae 
Definate Integration - By Partial Fraction 
Definate Integration - By e formula 
Definate Integration - By Substitution 
Definate Integration by properties - P2 
Definate Integration by properties - P3 
Definate Integration by properties - P4 
Definate Integration by properties - P6 
Definate Integration by properties - P7