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Misc 3 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▒〖𝐬𝐒𝐧⁑𝒙 𝒅𝒙〗 = [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^πŸπ…β–’γ€–π’”π’Šπ’β‘π’™ 𝒅𝒙〗 = [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 = πŸ’ square units

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.