Integration Full Chapter Explained - https://you.tube/Integration-Class-12

Last updated at Dec. 6, 2019 by Teachoo

Transcript

Ex7.10, 7 Evaluate the integrals using substitution −11 𝑑𝑥 𝑥2 + 2𝑥 + 5 we can write −11 𝑑𝑥 𝑥2 + 2𝑥 + 5= −11 𝑑𝑥 𝑥 + 2𝑥 + 1 + 4 = −11 𝑑𝑥 𝑥 + 12 + 22 Putting 𝑥+1=𝑡 Differentiating w.r.t.𝑥 𝑑𝑑𝑥 𝑥+1= 𝑑𝑡𝑑𝑥 1= 𝑑𝑡𝑑𝑥 𝑑𝑥=𝑑𝑡 Hence when 𝑥 varies from – 1 to 1 then 𝑡 varies from 0 to 2 Therefore, −11 𝑑𝑥 𝑥+12 + 22= 02 𝑑𝑡 𝑡2 + 22 = 12 tan−1 𝑡202 = 12 tan−1 22− 12 tan−1 02 = 12 tan−11− 12 tan−10 = 12 × 𝜋4−0 = 𝝅𝟖

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.