# Example 27 (iii) - Chapter 7 Class 12 Integrals

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 27 Evaluate the following integrals: (iii) 1 2 + 1 + 2 Step 1 :- = + 1 + 2 We can write the integrate as : + 1 + 2 = A + 1 + B + 2 + 1 + 2 = A + 2 + B + 1 + 1 + 2 By canceling denominators =A +2 +B +1 Therefore + 1 + 2 = 1 + 1 + 2 + 2 Integrating w.r.t. +1 +2 = 1 +1 + 2 +2 = +1 +2 +2 = +1 + +2 2 = +2 2 +1 = + 2 2 + 1 Hence = + 2 2 + 1 Step 2 :- 1 2 + 1 + 2 = 2 1 1 2 + 1 + 2 = 2 + 2 2 2 + 1 1 + 2 2 1 + 1 = 4 2 3 3 2 2 = 4 2 3 3 2 2 = 4 2 3 2 3 2 = 16 3 2 9 = 32 27 =

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
- 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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.