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  1. Chapter 8 Class 12 Application of Integrals
  2. Serial order wise

Transcript

Misc 5 Find the area bounded by the curve 𝑦=sin⁑π‘₯ between π‘₯=0 and π‘₯=2πœ‹ Area Required = Area OAB + Area BCD Area OAB = ∫_0^πœ‹β–’γ€–π‘¦ 𝑑π‘₯γ€— 𝑦→sin⁑π‘₯ = ∫_0^πœ‹β–’γ€–sin⁑π‘₯ 𝑑π‘₯γ€— = [βˆ’cos⁑π‘₯ ]_β–ˆ( @0)^πœ‹ =βˆ’ [cosβ‘πœ‹βˆ’cos⁑0 ] =βˆ’[βˆ’1βˆ’1] =βˆ’[βˆ’2] = 2 Area BCD = ∫_πœ‹^2πœ‹β–’γ€–π‘¦ 𝑑π‘₯γ€— = ∫_πœ‹^2πœ‹β–’γ€–sin⁑π‘₯ 𝑑π‘₯γ€— = [βˆ’cos⁑π‘₯ ]_β–ˆ( @ @πœ‹)^2πœ‹ =βˆ’ [cos⁑2πœ‹βˆ’cosβ‘πœ‹ ] =βˆ’[1βˆ’(βˆ’1)] = – 2 Since area cannot be negative, Area BCD = 2 Hence, Area Required = Area OAB + Area BCD = 2+2 = 4

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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.