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Last updated at Dec. 12, 2019 by Teachoo

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Ex 8.2 , 3 Find the area of the region bounded by the curves ๐ฆ=๐ฅ2+2, ๐ฆ=๐ฅ, ๐ฅ=0 and ๐ฅ=3 Here, ๐ฆ=๐ฅ2+2 ๐ฆโ2=๐ฅ^2 ๐ฅ^2=(๐ฆโ2) So, it is a parabola And, ๐ฅ=๐ฆ is a line x = 3 is a line x = 0 is the y-axis Finding point of intersection B & C Point B Point B is intersection of x = 3 and parabola Putting ๐ฅ=3 in ๐ฅ^2=(๐ฆโ2) 3^2=(๐ฆโ2) 9 = ๐ฆโ2 ๐ฆ=11 Hence, B = (3 , 11) Point C Point C is the intersection of x = 3 and x = y Putting ๐ฅ=3 in ๐ฅ=๐ฆ 3=๐ฆ i.e. ๐ฆ=3 Hence C = (3 , 3) Finding Area Area required = Area ABDO โ Area OCD Area ABDO Area ABDO = โซ_0^3โใ๐ฆ ๐๐ฅใ ๐ฆโ Equation of parabola AB ๐ฆ=๐ฅ^2+2 โด Area ABDO = โซ_0^3โใ๐ฆ ๐๐ฅใ = โซ_0^3โใ(๐ฅ^2+2) ๐๐ฅใ = [๐ฅ^3/3+2๐ฅ]_0^3 = [3^3/3+2 ร3โ0^3/3] = 9+6 = 15 Area OCD Area OCD = โซ_0^3โใ๐ฆ ๐๐ฅใ ๐ฆโ equation of line ๐ฆ=๐ฅ โด Area OCD = โซ_0^3โใ๐ฆ ๐๐ฅใ = โซ_0^3โใ๐ฅ ๐๐ฅใ = [๐ฅ^2/2]_0^3 =[3^2/2โ0^2/2] = 9/2 Area required = Area ABDO โ Area OCD = 15 โ 9/2 = ๐๐/๐ square units

About the Author

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.