Misc 44 - Value fo tan- 1 (2x - 1 / 1 + x - x2) dx is - Definate Integration by properties - P4

Slide32.JPG
Slide33.JPG

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

Transcript

Misc 44 Choose the correct answer The value of ﷐0﷮1﷮﷐﷐tan﷮−1﷯﷮﷐﷐2𝑥−1﷮1 + 𝑥 − ﷐𝑥﷮2﷯﷯﷯﷯﷯𝑑𝑥 is equal to (A) 1 (B) 0 (C) −1 (D) ﷐𝜋﷮4﷯ Let I=﷐0﷮1﷮﷐﷐tan﷮−1﷯﷮﷐﷐2𝑥−1﷮1 + 𝑥 − ﷐𝑥﷮2﷯﷯﷯﷯﷯𝑑𝑥 I=﷐0﷮1﷮﷐﷐tan﷮−1﷯﷮﷐﷐𝑥 + ﷐𝑥 − 1﷯﷮1 + 𝑥﷐1 − 𝑥﷯﷯﷯﷯﷯𝑑𝑥 I=﷐0﷮1﷮﷐﷐tan﷮−1﷯﷮﷐﷐𝑥 + ﷐𝑥 − 1﷯﷮1 + 𝑥﷐𝑥 − 1﷯﷯﷯﷯﷯𝑑𝑥 ∴ I=﷐0﷮1﷮﷐﷐tan﷮−1﷯ ﷐𝑥﷯+﷐tan﷮−1﷯﷐𝑥−1﷯﷯﷯ 𝑑𝑥 I=﷐0﷮1﷮﷐tan﷮−1﷯ ﷐𝑥﷯﷯ 𝑑𝑥+﷐0﷮1﷮﷐tan﷮−1﷯﷐𝑥−1﷯﷯ 𝑑𝑥 ∴ I=﷐0﷮1﷮﷐tan﷮−1﷯ ﷐1−𝑥﷯﷯ 𝑑𝑥+﷐0﷮1﷮﷐tan﷮−1﷯﷐1−𝑥−1﷯﷯ 𝑑𝑥 I=﷐0﷮1﷮﷐tan﷮−1﷯ −﷐𝑥−1﷯﷯ 𝑑𝑥+﷐0﷮1﷮﷐tan﷮−1﷯﷐−𝑥﷯﷯ 𝑑𝑥 I=−﷐0﷮1﷮﷐tan﷮−1﷯﷐𝑥−1﷯﷯ 𝑑𝑥−﷐0﷮1﷮﷐tan﷮−1﷯﷐𝑥﷯﷯𝑑𝑥 Adding (1) and (2) I+I =﷐0﷮1﷮﷐tan﷮−1﷯﷐𝑥﷯﷯ 𝑑𝑥+﷐0﷮1﷮﷐tan﷮−1﷯﷐𝑥−1﷯﷯𝑑𝑥−﷐0﷮1﷮﷐tan﷮−1﷯﷐𝑥﷯﷯𝑑𝑥−﷐0﷮1﷮﷐tan﷮−1﷯﷐𝑥−1﷯﷯𝑑𝑥 2I=0 ∴ I=0 Hence, correct answer is B.

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 provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail