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Ex 7.9, 10 - Chapter 7 Class 12 Integrals
Last updated at Dec. 20, 2019 by Teachoo
Transcript
Ex 7.9, 10 β«_0^1βππ₯/(1 + π₯2) Let F(π₯)=β«1βππ₯/(1 + π₯^2 ) =β«1β1/(1^2 + π₯^2 ) ππ₯ =1/1 .tan^(β1)β‘(π₯/1) =tan^(β1) π₯ Hence F(π₯)=tan^(β1) π₯ (Using β«1β1/(π₯^2 + π^2 ) ππ₯=1/π tan^(β1)β‘π₯) Now, β«_0^1βγππ₯/(1 + π₯^2 )=πΉ(1)βπΉ(0) γ =tan^(β1)β‘γ(1)βtan^(β1)β‘(0) γ =π/4β0 =π /π
Definite Integration - By Formulae
Ex 7.9, 1
Example 27 (i)
Ex 7.9, 3
Ex 7.9, 6
Ex 7.9, 2
Misc 29
Ex 7.9, 4
Ex 7.9, 5
Ex 7.9, 7
Ex 7.9, 8 Important
Ex 7.9, 17 Important
Ex 7.9, 12
Ex 7.9, 18
Misc 37
Misc 38 Important
Ex 7.10, 2 Important
Ex 7.9, 20 Important
Ex 7.9, 9
Ex 7.9, 10 You are here
Ex 7.9, 21 Important
Ex 7.9, 22
Ex 7.9, 14
Ex 7.9, 19 Important
Ex 7.10, 10 Important
Ex 7.10, 8
Misc 35
Misc 39
Ex 7.10, 3 Important
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.