# Example 13 - Chapter 8 Class 12 Application of Integrals

Last updated at Dec. 12, 2019 by Teachoo

Last updated at Dec. 12, 2019 by Teachoo

Transcript

Example 13 Find the area bounded by the curve π¦=cosβ‘π₯ between π₯=0 and π₯=2π Area Required = Area OAB + Area BCD + Area DEF x = π/2 Area OAB = β«_0^(π/( 2))βγπ¦ ππ₯γ π¦βcosβ‘π₯ = β«_0^(π/( 2))βγcosβ‘π₯ ππ₯γ = [sinβ‘π₯ ]_0^(π/2) =sinβ‘γπ/2βsinβ‘0 γ =1β0 =1 Area BCD = β«_(π/( 2))^(3π/( 2))βγπ¦ ππ₯γ = β«_(π/( 2))^(3π/( 2))βγcosβ‘π₯ ππ₯γ = [sinβ‘π₯ ]_(π/( 2))^(3π/( 2)) = sin 3π/( 2)βsinβ‘γπ/( 2)γ = β 1 β 1 = β2 Since area cannot be negative Area BCD = 2 Area DEF = β«_(3π/( 2))^2πβγπ¦ ππ₯γ = β«_(3π/( 2))^2πβγcosβ‘π₯ ππ₯γ = [sinβ‘π₯ ]_(3π/( 2))^2π =sinβ‘2π βsinβ‘γ3π/( 2)γ = 0β(β1) = 1 Therefore Area Required = Area OAB + Area BCD + Area DEF = 1 + 2 + 1 = 4 square unit

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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.