# Example 1 - Chapter 7 Class 12 Integrals

Last updated at Dec. 20, 2019 by Teachoo

Last updated at Dec. 20, 2019 by Teachoo

Transcript

Example 1 Write an anti derivative for each of the following functions using the method of inspection: (i) cosโก2๐ฅ We know that (๐ ๐๐ ๐ฅ)^โฒ=๐๐๐ ๐ฅ (๐ ๐๐ 2๐ฅ)^โฒ=๐๐๐ 2๐ฅร 2 (๐ ๐๐ 2๐ฅ)^โฒ=2๐๐๐ 2๐ฅ (๐ ๐๐ 2๐ฅ)^โฒ/2=๐๐๐ 2๐ฅ โด Anti Derivative of (cos 2x) is ๐/๐ (๐๐๐ ๐๐) Example 1 Write an anti derivative for each of the following functions using the method of inspection: (ii) 3๐ฅ^2+4๐ฅ^3 We know that Adding (1) and (2) (๐ฅ^3 )^โฒ+(๐ฅ^4 )^โฒ=3๐ฅ^2+4๐ฅ^3 Hence Anti derivative of is ๐^๐+๐^๐ (๐ฅ^3 )^โฒ=3๐ฅ^( 3โ1) (๐ฅ^3 )^โฒ=3๐ฅ^2 Also, (๐ฅ^4 )^โฒ=4๐ฅ^( 4โ1) (๐ฅ^4 )^โฒ=4๐ฅ^3 Example 1 Write an anti derivative for each of the following functions using the method of inspection: (iii) 1/๐ฅ, ๐ฅโ 0 We know that (logโก๐ฅ )^โฒ=1/( ๐ฅ) Hence Anti derivative of is ๐/๐

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.