Ex 7.11, 3 - Evaluate integral sin3/2 x dx / cos3/2 x  - Definate Integration by properties - P4

Slide6.JPG

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

Transcript

Ex 7.11, 3 By using the properties of definite integrals, evaluate the integrals : 0﷮ 𝜋﷮2﷯﷮ sin﷮ 3﷮2﷯﷯﷮𝑥﷯ 𝑑𝑥﷮ sin﷮ 3﷮2﷯﷯﷮𝑥﷯ + cos﷮ 3﷮2﷯﷯﷮𝑥﷯﷯﷯ Let I= 0﷮ 𝜋﷮2﷯﷮ sin﷮ 3﷮2﷯﷯ 𝑥﷮ sin﷮ 3﷮2﷯﷯ 𝑥 + cos﷮ 3﷮2﷯﷯﷮𝑥﷯﷯ 𝑑𝑥﷯ I= 0﷮ 𝜋﷮2﷯﷮ sin﷮ 3﷮2﷯﷯ 𝜋﷮2﷯ − 𝑥﷯﷮ sin﷮ 3﷮2﷯﷯ 𝜋﷮2﷯ − 𝑥﷯ + cos﷮ 3﷮2﷯﷯ 𝜋﷮2﷯ − 𝑥﷯﷯ 𝑑𝑥﷯ ∴ I= 0﷮ 𝜋﷮2﷯﷮ cos﷮ 3﷮2﷯﷯﷮𝑥﷯﷮ cos﷮ 3﷮2﷯﷯﷮𝑥﷯ + sin﷮ 3﷮2﷯﷯﷮𝑥﷯﷯ 𝑑𝑥﷯ Adding (1) and (2) i.e. (1) + (2) I+I= sin﷮ 3﷮2﷯﷯﷮𝑥﷯﷮ sin﷮ 3﷮2﷯﷯﷮𝑥﷯ + cos﷮ 3﷮2﷯﷯﷮𝑥﷯﷯ 𝑑𝑥+ 0﷮ 𝜋﷮2﷯﷮ cos﷮ 3﷮2﷯﷯﷮𝑥﷯﷮ cos﷮ 3﷮2﷯﷯﷮𝑥﷯ + sin﷮ 3﷮2﷯﷯﷮𝑥﷯﷯ 𝑑𝑥﷯ 2I= 0﷮ 𝜋﷮2﷯﷮ sin﷮ 3﷮2﷯﷯﷮𝑥﷯ + cos﷮ 3﷮2﷯﷯﷮𝑥﷯﷮ sin﷮ 3﷮2﷯﷯﷮𝑥﷯ + cos﷮ 3﷮2﷯﷯﷮𝑥﷯﷯﷯ 𝑑𝑥﷯ 2I= 0﷮ 𝜋﷮2﷯﷮ 𝑑𝑥﷯ I= 1﷮2﷯ 0﷮ 𝜋﷮2﷯﷮ 𝑑𝑥﷯ I= 1﷮2﷯ 𝑥﷯﷮0﷮ 𝜋﷮2﷯﷯ I= 1﷮2﷯ 𝜋﷮2﷯−0﷯ I= 𝜋﷮4﷯

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.