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Ex 7.9, 1 - Chapter 7 Class 12 Integrals
Last updated at December 16, 2024 by Teachoo
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
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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 7.9, 1 Evaluate the integrals using substitution ā«_0^1āćš„/(š„^2 + 1) šš„ć We need to find ā«_š^šāćš/(š^š + š) š šć Let š=š^š+š Differentiating w.r.t. š„ šš”/šš„=š/šš„ (š„^2+1) šš”/šš„=2š„ š š/šš=š š Now, when š varies from 0 to 1 then š varies from 1 to 2 Therefore ā«_š^šāćš/(š^š+š) š š=ā«_š^šāćš/š š š/ššćć =1/2 ā«_1^2āšš”/š” =š/š [ššš|š|]_š^š =1/2 [ššš|2|āššš|1|] =1/2 [ššš|2|ā0] =1/2 ššš|2| =š/š ššš š
