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

Last updated at Dec. 20, 2019 by Teachoo

Transcript

Ex 7.10, 5 Evaluate the integrals using substitution β«_0^(π/2 )βsinβ‘π₯/(1 + cos^2β‘π₯ )β‘γ ππ₯γ β«_0^(π/2 )βsinβ‘π₯/(1 + cos^2β‘π₯ )β‘γ ππ₯γ Put cos π₯=π‘ Differentiating w.r.t.π₯ βsinβ‘π₯=ππ‘/ππ₯ ππ₯=(βππ‘)/sinβ‘π₯ Hence when π₯ varies from 0 to π/2, π‘ varies from 1 to 0 Therefore, we can write β«_0^(π/2)βsinβ‘π₯/(1+γ cos^2γβ‘π₯ ) ππ₯=β«_1^0βγsinβ‘π₯/(1 + π‘^2 ) ((βππ‘)/sinβ‘π₯ ) γ =ββ«_1^0βππ‘/(1 + π‘^2 ) =β[tan^(β1)β‘π‘ ]_1^0 =β[tan^(β1)β‘γ(0)βtan^(β1)β‘(1) γ ] =β[0βπ/4] =β[βπ/4] =π /π

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.