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Last updated at Dec. 20, 2019 by Teachoo

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Ex 7.3, 1 Find the integral of sin2 (2π₯ + 5) β«1βγsin2 (2π₯ + 5) γ ππ₯ =β«1β(1 β γπππ 2γβ‘(2π₯ + 5))/2 ππ₯ =1/2 β«1βγ1βcosβ‘(4π₯+10) γ ππ₯ =1/2 [β«1β1 ππ₯ββ«1βcosβ‘(4π₯+10) ππ₯] We know that cos 2π=1β2 sin^2β‘π 2 sin^2 π=1βcosβ‘2π sin^2 π=1/2 [1βcosβ‘2π ] Replace π by (2π₯+5) sin^2 (2π₯+5)=(1 β cosβ‘2(2π₯ + 5))/2 (As β«1βcosβ‘(ππ₯+π) ππ₯=sinβ‘(ππ₯ + π)/π+πΆ) =1/2 [π₯β sinβ‘(4π₯ + 10)/4 +πΆ] =π/π β π/π πππβ‘(ππ+ππ)+πͺ

Integration using trigo identities - 2x formulae

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.