Integration Full Chapter Explained - https://you.tube/Integration-Class-12

Last updated at Dec. 23, 2019 by Teachoo

Transcript

Misc 38 Prove that β«_0^(π/4)βγ2 tanγ^3β‘π₯ ππ₯=1βlogβ‘2 Solving L.H.S 2β«_0^(π/4)βγ tanγ^3β‘π₯ ππ₯ = 2β«_0^(π/4)βγ tan π₯ tanγ^2β‘π₯ ππ₯ = 2β«_0^(π/4)βγ tan π₯ (secγ^2β‘γπ₯β1)γ ππ₯ = 2β«_0^(π/4)βγ tan π₯ secγ^2β‘π₯ ππ₯β 2β«_0^(π/4)βtanβ‘γπ₯ ππ₯γ π°_π = 2β«_π^(π /π)βγ πππ§ π πππγ^πβ‘π π π Let t = tan x ππ‘/ππ₯ = γπ ππγ^2 x dt = γπ ππγ^2x dx Substituting, 2β«1_0^1βγπ‘ ππ‘γ = 2 [π‘^2/2]_0^1 = 2 (1/2β0) =1 π°_π= 2β«_π^(π /π)βπππβ‘γπ π πγ 2β«_π^(π /π)βπππβ‘γπ π πγ = 2 ["log" |saecβ‘π₯ |]_0^(π/4) = 2 ("log" β2β0) = 2 (log 2^(1/2)) = 2 (1/2 "log " 2) = log 2 Hence, = πΌ_1βπΌ_2 = 1 β log 2 = R.H.S Hence, proved.

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

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Ex 7.9, 8 Important

Ex 7.9, 17 Important

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Ex 7.9, 18

Misc 37

Misc 38 Important You are here

Ex 7.10, 2 Important

Ex 7.9, 20 Important

Ex 7.9, 9

Ex 7.9, 10

Ex 7.9, 21 Important

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Ex 7.9, 14

Ex 7.9, 19 Important

Ex 7.10, 10 Important

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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.