Misc 7 - Integrate sin x / sin (x - a) - Chapter 7 Class 12 - Miscellaneous

Misc 7 last slide.jpg

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

Transcript

Misc 7 Integrate the function sin⁑π‘₯/sin⁑(π‘₯ βˆ’ π‘Ž) Let I = ∫1β–’sin⁑π‘₯/sin⁑(π‘₯ βˆ’ π‘Ž) 𝑑π‘₯ Put t = π‘₯ βˆ’ π‘Ž Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑𝑑/𝑑π‘₯ = 𝑑(π‘₯ βˆ’ π‘Ž)/𝑑π‘₯ 𝑑𝑑/𝑑π‘₯ = 1 𝑑π‘₯ = 𝑑𝑑 Therefore ∫1β–’γ€–sin 〗⁑(𝑑 + π‘Ž)/sin⁑𝑑 𝑑𝑑 = ∫1β–’(sin⁑𝑑 cosβ‘π‘Ž + cos⁑𝑑 sinβ‘π‘Ž)/sin⁑𝑑 𝑑𝑑 = ∫1β–’((sin⁑𝑑 cosβ‘π‘Ž)/sin⁑𝑑 + (cos⁑𝑑 sinβ‘π‘Ž)/sin⁑𝑑 ) 𝑑𝑑 = ∫1β–’cosβ‘π‘Ž 𝑑𝑑 + ∫1β–’cot⁑𝑑 sinβ‘π‘Ž 𝑑𝑑 = cosβ‘π‘Ž ∫1▒𝑑𝑑 + sinβ‘π‘Ž ∫1β–’cot⁑𝑑 𝑑𝑑 = t cos a + sin a log |sin⁑𝑑 | + C Putting back t = x – a = (x – a) cos a + sin a |sin⁑〖(π‘₯βˆ’π‘Ž)γ€— | + C = sin a log |sin⁑〖(π‘₯βˆ’π‘Ž)γ€— | + x cos a βˆ’ a cos a + C = sin a log |𝐬𝐒𝐧⁑〖(π’™βˆ’π’‚)γ€— | + x cos a + 𝐂_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 9 years. He provides courses for Maths and Science at Teachoo.