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Ex 7.2, 1 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
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
Transcript
Ex 7.2, 1 Integrate the function: 2𝑥/(1 + 𝑥2) We need to find ∫1▒𝟐𝒙/(𝟏 + 𝒙𝟐) 𝒅𝒙 Let 𝟏 + 𝒙𝟐 = 𝒕 Differentiating 𝑤.𝑟.𝑡.𝑥 2𝑥=𝑑𝑡/𝑑𝑥 𝒅𝒙=𝒅𝒕/𝟐𝒙 Thus, our equation becomes ∫1▒𝟐𝒙/(𝟏 + 𝒙𝟐) 𝒅𝒙 =∫1▒2𝑥/𝑡 . 𝑑𝑡/2𝑥 =∫1▒𝑑𝑡/𝑡 = log |𝒕|+𝑪 Putting t = 1 + x2 = log |1+𝑥^2 |+𝐶 = log (𝟏+𝒙^𝟐 )+𝑪 (∫1▒〖1/𝑥 𝑑𝑥〗=log|𝑥|+𝐶) (Since 1+𝑥^2 is always positive)
