Ex 7.3, 2 - Integrate sin 3x cos 4x - Class 12 CBSE - Ex 7.3

Slide4.JPG

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

Transcript

Ex 7.3, 2 sin⁡3 𝑥 cos⁡4𝑥 We know that 2 sin A cos B=sin 𝐴+𝐵﷯+ sin﷮ 𝐴−𝐵﷯﷯ sin A cos B= 1﷮2﷯ sin﷮ 𝐴+𝐵﷯﷯+ sin﷮ 𝐴−𝐵﷯﷯﷯ Replace A by 3𝑥 & B by 4𝑥 sin 3𝑥 cos 4𝑥= 1﷮2﷯ sin﷮ 3𝑥+4𝑥﷯﷯+ sin﷮ 3𝑥−4𝑥﷯﷯﷯ sin 3𝑥 cos 4𝑥= 1﷮2﷯ sin﷮7𝑥﷯+ sin﷮ −𝑥﷯﷯﷯ sin 3𝑥 cos 4𝑥= 1﷮2﷯ sin﷮7𝑥﷯− sin﷮𝑥﷯﷯ Now, ﷮﷮ sin﷮3𝑥﷯ cos﷮4𝑥﷯﷯𝑑𝑥= ﷮﷮ 1﷮2﷯ sin﷮7𝑥﷯− sin﷮𝑥﷯﷯﷯𝑑𝑥 = 1﷮2﷯ ﷮﷮ sin﷮7𝑥﷯﷯𝑑𝑥− ﷮﷮ sin﷮𝑥﷯﷯𝑑𝑥﷯ Now, ﷮﷮ sin﷮3𝑥﷯ cos﷮4𝑥﷯﷯﷯𝑑𝑥= 1﷮2﷯ ﷮﷮ sin﷮7𝑥﷯﷯𝑑𝑥− ﷮﷮ sin﷮𝑥﷯﷯𝑑𝑥﷯ = 1﷮2﷯ − cos﷮7𝑥﷯﷮7﷯ + cos﷮𝑥﷯﷯+𝐶 = −𝟏﷮𝟏𝟒﷯ 𝒄𝒐𝒔﷮𝟕𝒙﷯+ 𝟏﷮𝟐﷯ 𝐜𝐨𝐬﷮𝒙﷯+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 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
Jail