Ex 7.3, 6 - Integrate sin x sin 2x sin 3x - CBSE - Integration using trigo identities - CD and CD inv formulae

Slide16.JPG
Slide17.JPG Slide18.JPG Slide19.JPG

  1. Class 12
  2. Important Question for exams Class 12

Transcript

Ex 7.3, 6 𝑠𝑖𝑛 𝑥 sin⁡2𝑥 sin⁡3𝑥 ﷮﷮ sin﷮𝑥 sin﷮2𝑥 sin﷮3𝑥﷯﷯﷯﷯ 𝑑𝑥 = ﷮﷮ sin﷮𝑥﷯ sin﷮2𝑥﷯﷯ sin﷮3𝑥﷯﷯ 𝑑𝑥 We know that 2 sin﷮𝐴﷯ sin﷮𝐵﷯=− cos﷮ 𝐴+𝐵﷯﷯+ cos﷮ 𝐴−𝐵﷯﷯ sin﷮𝐴﷯ sin﷮𝐵﷯= 1﷮2﷯ − cos﷮ 𝐴+𝐵﷯﷯+ cos﷮ 𝐴−𝐵﷯﷯﷯ sin﷮𝐴﷯ sin﷮𝐵﷯= 1﷮2﷯ cos﷮ 𝐴−𝐵﷯﷯− cos﷮ 𝐴+𝐵﷯﷯﷯ Replace A by 𝑥 & B by 2𝑥 sin﷮𝑥﷯ sin﷮3𝑥﷯= 1﷮2﷯ cos﷮ 𝑥−2𝑥﷯﷯− cos﷮ 𝑥+2𝑥﷯﷯﷯ sin﷮𝑥﷯ sin﷮3𝑥﷯ = 1﷮2﷯ cos﷮ −𝑥﷯﷯− cos﷮ 3𝑥﷯﷯﷯ sin﷮𝑥﷯ sin﷮3𝑥﷯ = 1﷮2﷯ cos﷮ 𝑥﷯﷯− cos﷮3𝑥﷯﷯ Thus, ﷮﷮ sin﷮𝑥 sin﷮2𝑥 sin﷮3𝑥﷯﷯﷯﷯ 𝑑𝑥 = ﷮﷮ 1﷮2﷯ cos﷮𝑥﷯− cos﷮3𝑥﷯﷯﷯﷯ . sin﷮3𝑥﷯.𝑑𝑥 = 1﷮2﷯ ﷮﷮ cos﷮𝑥﷯− cos﷮3𝑥﷯﷯﷯ sin﷮3𝑥﷯ 𝑑𝑥 = 1﷮2﷯ ﷮﷮ cos﷮𝑥﷯. sin﷮3𝑥﷯− cos﷮3𝑥﷯. sin﷮3𝑥﷯﷯﷯﷯𝑑𝑥 = 1﷮2﷯ ﷮﷮ cos﷮𝑥﷯. sin﷮3𝑥﷯﷯ 𝑑𝑥− ﷮﷮ cos﷮3𝑥﷯. sin﷮3𝑥﷯﷯ 𝑑𝑥﷯ = 1﷮4﷯ − cos﷮4𝑥﷯﷮4﷯ + cos﷮2𝑥﷯﷮2﷯ − − cos﷮6𝑥﷯﷮6﷯﷯﷯+𝐶 = 𝟏﷮𝟒﷯ 𝒄𝒐𝒔﷮𝟔𝒙﷯﷮𝟔﷯ − 𝒄𝒐𝒔﷮𝟒𝒙﷯﷮𝟒﷯ + 𝒄𝒐𝒔﷮𝟐𝒙﷯﷮𝟐﷯ ﷯+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 has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.