Misc 38 - Prove that 2 tan3 x dx = 1 - log2 - CBSE - Definate Integration - By Formulae

Misc Part - 4.jpg
Slide13.JPG

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

Transcript

Misc 38 Prove that ﷐0﷮﷐𝜋﷮4﷯﷮﷐﷐2 tan﷮3﷯﷮𝑥﷯﷯ 𝑑𝑥=1−﷐log﷮2﷯ Solving L.H.S : 2﷐0﷮﷐𝜋﷮4﷯﷮﷐﷐ tan﷮3﷯﷮𝑥﷯﷯ 𝑑𝑥 = 2﷐0﷮﷐𝜋﷮4﷯﷮﷐﷐ tan 𝑥 tan﷮2﷯﷮𝑥﷯﷯ 𝑑𝑥 = 2﷐0﷮﷐𝜋﷮4﷯﷮﷐﷐ tan 𝑥 (sec﷮2﷯﷮𝑥−1)﷯﷯ 𝑑𝑥 = 2﷐0﷮﷐𝜋﷮4﷯﷮﷐﷐ tan 𝑥 sec﷮2﷯﷮𝑥﷯﷯ 𝑑𝑥− 2﷐0﷮﷐𝜋﷮4﷯﷮﷐tan﷮𝑥 𝑑𝑥﷯﷯ Hence, = ﷐𝐼﷮1﷯−﷐𝐼﷮2﷯ = 1 − log 2 = R.H.S Hence, proved.

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.