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Example 13 - Find area bounded by y = cos x, x = 0, 2pi - Examples

Example 13 - Chapter 8 Class 12 Application of Integrals - Part 2
Example 13 - Chapter 8 Class 12 Application of Integrals - Part 3

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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 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.