Example 7 - Find intgeral (i) cos2 x dx (ii) sin 2x cos 3x - Integration using trigo identities - CD and CD inv formulae

Slide30.JPG
Slide31.JPG Slide32.JPG Slide33.JPG Slide34.JPG Slide35.JPG Slide36.JPG Slide37.JPG

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

Transcript

Example 7 Find (i) cos 2 cos 2 = cos 2 + 1 2 = 1 2 cos 2 +1 = 1 2 cos 2 + 1 Thus, cos 2 = 1 2 cos 2 + 1 = 1 2 1 2 sin 2 + 1+ + 2 = 1 2 1 2 sin 2 + + 1+ 2 = 1 4 sin 2 + 1 2 + = + + Example 7 Find (ii) sin 2 cos 3 Now sin 2 cos 3 = 1 2 sin 5 sin = 1 2 sin 5 sin Thus, sin 2 cos 3 = 1 2 sin 5 sin = 1 2 1 5 cos 5 + 1 5 1 cos + 2 = 1 2 1 5 cos 5 + cos + 1 5 1 2 = 1 2 1 5 cos 5 + cos + = + + Example 7 Find (iii) sin 3 sin 3 = 3 sin sin 3 4 = 1 4 3 sin sin 3 = 1 4 3 sin sin 3 Thus, sin 3 = 1 4 3 sin sin 3 = 1 4 3 cos + 2 1 3 cos 3 + 1 3 1 = 1 4 3 cos +3 2+ 1 3 cos 3 + 1 3 1 = 1 4 3 cos + 1 3 cos 3 + 3 2 1 3 1 = 3 4 cos + 1 12 cos 3 + 1 4 3 2 1 3 1 = + +

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.