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Misc 5 - Find area bounded by y = sin x between x = 0, 2pi

Misc 5 - Chapter 8 Class 12 Application of Integrals - Part 2
Misc 5 - Chapter 8 Class 12 Application of Integrals - Part 3

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.