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Ex 7.9, 1 - Chapter 7 Class 12 Integrals
Last updated at August 18, 2026 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
-
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 7.9, 1 Evaluate the integrals using substitution ∫_0^1▒〖𝑥/(𝑥^2 + 1) 𝑑𝑥〗 We need to find ∫_𝟎^𝟏▒〖𝒙/(𝒙^𝟐 + 𝟏) 𝒅𝒙〗 Let 𝒕=𝒙^𝟐+𝟏 Differentiating w.r.t. 𝑥 𝑑𝑡/𝑑𝑥=𝑑/𝑑𝑥 (𝑥^2+1) 𝑑𝑡/𝑑𝑥=2𝑥 𝒅𝒕/𝟐𝒙=𝒅𝒙 Now, when 𝒙 varies from 0 to 1 then 𝒕 varies from 1 to 2 Therefore ∫_𝟎^𝟏▒〖𝒙/(𝒙^𝟐+𝟏) 𝒅𝒙=∫_𝟏^𝟐▒〖𝒙/𝒕 𝒅𝒕/𝟐𝒙〗〗 =1/2 ∫_1^2▒𝑑𝑡/𝑡 =𝟏/𝟐 [𝒍𝒐𝒈|𝒕|]_𝟏^𝟐 =1/2 [𝑙𝑜𝑔|2|−𝑙𝑜𝑔|1|] =1/2 [𝑙𝑜𝑔|2|−0] =1/2 𝑙𝑜𝑔|2| =𝟏/𝟐 𝒍𝒐𝒈 𝟐
