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Last updated at Dec. 20, 2019 by Teachoo

Transcript

Ex 7.9, 17 β«_0^(π/4)β(2 sec^2β‘π₯+π₯^3+2) ππ₯ Let F(π₯)=β«1βγ(2 sec^2β‘γπ₯+π₯^3+2γ ) ππ₯γ =2β«1βγsec^2β‘γπ₯ ππ₯γ+β«1βγπ₯^3 ππ₯+β«1βγ2 ππ₯γγγ =2 tanβ‘γπ₯+π₯^4/4+2π₯γ Hence F(π₯)=2 tanβ‘γπ₯+π₯^4/4+2π₯γ Now, β«_0^(π/4)βγ(2π ππ^2 π₯+π₯^3+2)ππ₯=πΉ(π/4)βπΉ(0) γ =[2π‘ππ π/4+(π/4)^4/4+2 π/4]β[2π‘ππ(0)+(0)^4/4+2 Γ0] =2π‘ππ π/4+π^4/4^4 Γ 1/4+π/2β[2Γ0+0+0] =2 Γ1+π^4/4^5 +π/2β0 =π+π ^π/ππππ+π /π

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 You are here

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

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.