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Ex 7.4, 2 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Integration by specific formulaes - Formula 6
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
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Transcript
Ex 7.4, 2(Method 1) 1/√(1 + 4𝑥^2 ) ∫1▒1/√(1 + 4𝑥^2 ) 𝑑𝑥 =∫1▒1/√(4 (1/4 + 𝑥^2 ) ) . 𝑑𝑥 =∫1▒1/(√4 √(1/4 + 𝑥^2 )) . 𝑑𝑥 =1/2 ∫1▒1/√(𝑥^2 + 1/4) . 𝑑𝑥 =1/2 log|𝑥+√(4𝑥^2 + 1)/2|+𝐶 =1/2 log|(2𝑥 + √(4𝑥^2 + 1))/2|+𝐶 =1/2 [log|2𝑥 + √(1+4𝑥^2 ) |−log2 ]+𝐶 =1/2 log|2𝑥 + √(1+4𝑥^2 ) |−1/2 log2+𝐶 =𝟏/𝟐 𝒍𝒐𝒈|𝟐𝒙 + √(𝟏+𝟒𝒙^𝟐 ) |+𝑪
