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

Transcript

Ex 8.2 , 3 Find the area of the region bounded by the curves ๐‘ฆ=๐‘ฅ2+2, ๐‘ฆ=๐‘ฅ, ๐‘ฅ=0 and ๐‘ฅ=3 Here, ๐‘ฆ=๐‘ฅ2+2 ๐‘ฆโˆ’2=๐‘ฅ^2 ๐‘ฅ^2=(๐‘ฆโˆ’2) So, it is a parabola And, ๐‘ฅ=๐‘ฆ 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 ๐‘ฅ=3 in ๐‘ฅ^2=(๐‘ฆโˆ’2) 3^2=(๐‘ฆโˆ’2) 9 = ๐‘ฆโˆ’2 ๐‘ฆ=11 Hence, B = (3 , 11) Point C Point C is the intersection of x = 3 and x = y Putting ๐‘ฅ=3 in ๐‘ฅ=๐‘ฆ 3=๐‘ฆ i.e. ๐‘ฆ=3 Hence C = (3 , 3) Finding Area Area required = Area ABDO โ€“ Area OCD Area ABDO Area ABDO = โˆซ_0^3โ–’ใ€–๐‘ฆ ๐‘‘๐‘ฅใ€— ๐‘ฆโ†’ Equation of parabola AB ๐‘ฆ=๐‘ฅ^2+2 โˆด Area ABDO = โˆซ_0^3โ–’ใ€–๐‘ฆ ๐‘‘๐‘ฅใ€— = โˆซ_0^3โ–’ใ€–(๐‘ฅ^2+2) ๐‘‘๐‘ฅใ€— = [๐‘ฅ^3/3+2๐‘ฅ]_0^3 = [3^3/3+2 ร—3โˆ’0^3/3] = 9+6 = 15 Area OCD Area OCD = โˆซ_0^3โ–’ใ€–๐‘ฆ ๐‘‘๐‘ฅใ€— ๐‘ฆโ†’ equation of line ๐‘ฆ=๐‘ฅ โˆด Area OCD = โˆซ_0^3โ–’ใ€–๐‘ฆ ๐‘‘๐‘ฅใ€— = โˆซ_0^3โ–’ใ€–๐‘ฅ ๐‘‘๐‘ฅใ€— = [๐‘ฅ^2/2]_0^3 =[3^2/2โˆ’0^2/2] = 9/2 Area required = Area ABDO โ€“ Area OCD = 15 โ€“ 9/2 = ๐Ÿ๐Ÿ/๐Ÿ square units

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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.