Integration Full Chapter Explained - Integration Class 12 - Everything you need

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 27 Evaluate the following integrals: (ii) 4 9 30 3 2 2 Step 1 :- 30 3 2 2 Let 30 3 2 = Differentiating w.r.t. both sides 30 3 2 = 3 2 3 2 1 = 3 2 1 2 = = 3 2 1 2 = 2 3 Therefore, our equation becomes 30 3 2 2 = 2 2 3 = 2 3 2 = 2 3 2 = 2 3 2 + 1 2 + 1 = 2 3 1 1 = 2 3 1 = 2 3 Putting = 30 3 2 = 2 3 30 3 2 Hence F = 2 3 30 3 2 Step 2 :- 4 9 30 3 2 = 9 4 = 2 3 30 9 3 2 2 3 30 4 3 2 = 2 3 30 3 2 2 3 2 3 30 2 2 2 3 = 2 3 1 30 3 3 1 30 2 3 = 2 3 1 30 27 1 30 8 = 2 3 1 3 1 22 = 2 3 22 3 3 22 = 2 3 19 66 = 19 3 (33) =

Definite Integration - By Substitution

Chapter 7 Class 12 Integrals

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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.