web analytics

Ex 7.3, 10 - Integrate sin4 x  - Chapter 7 Class 12 - Integration using trigo identities - 2x formulae

Slide27.JPG
Slide28.JPG

  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
Ask Download

Transcript

Ex 7.3, 10 𝑠𝑖𝑛4 𝑥 ﷮﷮ sin﷮4﷯﷮𝑥﷯﷯ 𝑑𝑥 = ﷮﷮ sin﷮2﷯﷮𝑥﷯﷯﷮2﷯﷯ 𝑑𝑥 = ﷮﷮ 1 − cos﷮2𝑥﷯﷮2﷯﷯﷮2﷯﷯ 𝑑𝑥 = 1﷮4﷯ ﷮﷮ 1− cos﷮2𝑥﷯﷯﷮2﷯﷯ 𝑑𝑥 = 1﷮4﷯ ﷮﷮ 1﷯﷮2﷯+ cos﷮2𝑥﷯﷯﷮2﷯−2 1﷯ cos﷮2𝑥﷯﷯﷯﷯ 𝑑𝑥 = 1﷮4﷯ ﷮﷮ 1+ cos﷮2﷯﷮2𝑥﷯−2 cos﷮2𝑥﷯﷯﷯ 𝑑𝑥 = 1﷮4﷯ ﷮﷮ 1+ 1 + cos﷮4𝑥﷯﷮2﷯−2 cos﷮2𝑥﷯﷯﷯ 𝑑𝑥 = 1﷮4﷯ ﷮﷮1﷯ 𝑑𝑥+ 1﷮8﷯ ﷮﷮ 1+ cos﷮4𝑥﷯﷯﷯𝑑𝑥− 2﷮4﷯ ﷮﷮ cos﷮2𝑥﷯﷯𝑑𝑥 = 1﷮4﷯ ﷮﷮1﷯ 𝑑𝑥+ 1﷮8﷯ ﷮﷮1﷯𝑑𝑥+ 1﷮8﷯ ﷮﷮ cos﷮4𝑥﷯﷯𝑑𝑥− 1﷮2﷯ ﷮﷮ cos﷮2𝑥﷯﷯𝑑𝑥 = 𝑥﷮4﷯ + 𝑥﷮8﷯ + 1﷮8﷯ sin﷮4𝑥﷯﷮4﷯ − 1﷮2﷯ sin﷮2𝑥﷯﷮2﷯ +𝐶 = 2𝑥 + 𝑥﷮8﷯ + 1﷮32﷯ sin﷮4𝑥﷯− 1﷮4﷯ sin﷮2𝑥﷯+𝐶 = 𝟑𝒙﷮𝟖﷯− 𝟏﷮𝟒﷯ 𝒔𝒊𝒏﷮𝟐𝒙﷯++ 𝟏﷮𝟑𝟐﷯ 𝒔𝒊𝒏﷮𝟒𝒙﷯𝑪

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail