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

Transcript

Example 13 Find the area bounded by the curve 𝑦=cos⁑π‘₯ between π‘₯=0 and π‘₯=2πœ‹ Area Required = Area OAB + Area BCD + Area DEF x = πœ‹/2 Area OAB = ∫_0^(πœ‹/( 2))▒〖𝑦 𝑑π‘₯γ€— 𝑦→cos⁑π‘₯ = ∫_0^(πœ‹/( 2))β–’γ€–cos⁑π‘₯ 𝑑π‘₯γ€— = [sin⁑π‘₯ ]_0^(πœ‹/2) =sinβ‘γ€–πœ‹/2βˆ’sin⁑0 γ€— =1βˆ’0 =1 Area BCD = ∫_(πœ‹/( 2))^(3πœ‹/( 2))▒〖𝑦 𝑑π‘₯γ€— = ∫_(πœ‹/( 2))^(3πœ‹/( 2))β–’γ€–cos⁑π‘₯ 𝑑π‘₯γ€— = [sin⁑π‘₯ ]_(πœ‹/( 2))^(3πœ‹/( 2)) = sin 3πœ‹/( 2)βˆ’sinβ‘γ€–πœ‹/( 2)γ€— = – 1 – 1 = –2 Since area cannot be negative Area BCD = 2 Area DEF = ∫_(3πœ‹/( 2))^2πœ‹β–’γ€–π‘¦ 𝑑π‘₯γ€— = ∫_(3πœ‹/( 2))^2πœ‹β–’γ€–cos⁑π‘₯ 𝑑π‘₯γ€— = [sin⁑π‘₯ ]_(3πœ‹/( 2))^2πœ‹ =sin⁑2πœ‹ βˆ’sin⁑〖3πœ‹/( 2)γ€— = 0βˆ’(βˆ’1) = 1 Therefore Area Required = Area OAB + Area BCD + Area DEF = 1 + 2 + 1 = 4 square unit

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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.