Subscribe to our Youtube Channel - https://www.youtube.com/channel/UCZBx269Tl5Os5NHlSbVX4Kg

Last updated at Dec. 20, 2019 by Teachoo

Transcript

Ex 7.10, 8 Evaluate the integrals using substitution โซ_1^(2 )โใ (1/๐ฅ โ1/(2๐ฅ^2 )) ใ ๐^2๐ฅ ๐๐ฅ Let ๐ก=2๐ฅ ๐๐ก/๐๐ฅ=2 ๐๐ก/2=๐๐ฅ Thus, when x varies from 1 to 2, t varies from 2 to 4 Substituting, โซ_1^(2 )โใ (1/๐ฅ โ1/(2๐ฅ^2 )) ใ ๐^2๐ฅ ๐๐ฅ = โซ_2^4โใ๐^๐ก (1/(๐ก/2)โ1/(2ใ (๐ก/2)ใ^2 )) ใ ๐๐ก/2 =โซ_2^4โใ๐^๐ก (2/๐กโ4/(2๐ก^2 )) ใ ๐๐ก/2 =โซ_2^4โใ๐^๐ก (1/๐กโ2/๐ก^2 ) ใ ๐๐ก It is of the form โซ1โใ๐^๐ฅ [๐(๐ฅ)+๐^โฒ (๐ฅ)] ใ ๐๐ฅ=๐^๐ฅ ๐(๐ฅ)+๐ถ Where ๐(๐ฅ)=1/๐ก ๐^โฒ (๐ฅ)= (โ1)/๐ก^2 Hence, our equation becomes โซ_2^4โใ๐^๐ก (1/๐กโ2/๐ก^2 ) ใ ๐๐ก = [๐^๐กร1/๐ก]_2^4 = (๐^4/4โ๐^2/2) = (๐^๐ (๐^๐ โ ๐))/๐

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

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 You are here

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.