Example 4 - Chapter 8 Class 12 Application of Integrals
Last updated at April 16, 2024 by Teachoo
Area bounded by curve and horizontal or vertical line
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Ex 8.1, 4 (MCQ) Important
Misc 1 (i)
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Area bounded by curve and horizontal or vertical line
Last updated at April 16, 2024 by Teachoo
Example 4 Find the area bounded by the curve π¦=cosβ‘π₯ between π₯=0 and π₯=2πArea OAB = β«_0^(π/( 2))βγπ¦ ππ₯γ π¦βcosβ‘π₯ = β«_π^(π /( π))βγπππβ‘π π πγ = [sinβ‘π₯ ]_0^(π/2) =sinβ‘γπ/2βsinβ‘0 γ =1β0 =π Area BCD = β«_(π/( 2))^(3π/( 2))βγπ¦ ππ₯γ = β«_(π /( π))^(ππ /( π))βγπππβ‘π π πγ = [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«_(ππ /( π))^ππ βγπππβ‘π π πγ = [sinβ‘π₯ ]_(3π/( 2))^2π =sinβ‘2π βsinβ‘γ3π/( 2)γ = 0β(β1) = π Therefore Area Required = Area OAB + Area BCD + Area DEF = 1 + 2 + 1 = 4 square unit