# Ex 7.5, 8 - Chapter 7 Class 12 Integrals

Last updated at July 11, 2018 by Teachoo

Last updated at July 11, 2018 by Teachoo

Transcript

Ex 7.5, 8 1 2 ( + 2) We can write the integrand as 1 2 ( + 2) = 1 + 1 2 + + 2 1 2 ( + 2) = 1 + 2 + + 2 + 1 2 1 + 1 2 + 3 By cancelling denominator = 1 +2 + +2 + 1 2 Putting x = 2, in (1) 2 = A 2 1 2+2 + B 2+2 + C 2 1 2 2 = A 0+B 0+C 3 2 2 = 9C C = 2 9 Putting x = 1, in (1) 1 = A 1 1 1+2 + B 1+2 + C 1 1 2 1 = A 0 + B 3 + C 1 1 2 1 = 3B B = 1 3 Putting x = 0, in (1) 0= 0 1 0+2 + 0+2 + 0 1 2 0= 1 2 +2 + 0= 2 + 2 3 2 9 0= 2 + 4 9 2 = 4 9 = 4 18 = 2 9 Hence we can write 1 2 ( + 2) = 2 9 1 + 1 3 1 2 + 2 9 + 2 = 2 9 1 + 1 3 1 2 + 2 9 + 2 = 2 9 1 + 1 3 1 2 + 2 9 + 2 = 2 9 log 1 + 1 3 1 1 2 9 log +2 + = 2 9 log 1 2 9 log +2 1 3 1 + = 2 9 log 1 log +2 1 3 1 + = + +

Integration by partial fraction - Type 4

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.