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

Transcript

Ex 8.2 , 5 Using integration find the area of the triangular region whose sides have the equations ๐‘ฆ=2๐‘ฅ+1, ๐‘ฆ=3๐‘ฅ+1 and ๐‘ฅ=4 Lets Draw the figure & x = 4 Therefore, Required Area = Area ABC Finding point of Intersection B & C For B B is intersection of y = 3x + 1 & x = 4 Putting x = 4 in y = 3x + 1 y = 3(4) + 1 = 13 So, B(4, 13) For C C is intersection of y = 2x + 1 & x = 4 Putting x = 4 in y = 2x + 1 y = 2(4) + 1 = 9 So, C(4, 9) Finding Area Required Area ABC = Area OABD โ€“ Area OACD Area OABD Area OABD = โˆซ1_0^4โ–’ใ€–๐‘ฆ ๐‘‘๐‘ฅใ€— Here, y = 3x + 1 Area OABD = โˆซ1_0^4โ–’ใ€–(3๐‘ฅ+1) ๐‘‘๐‘ฅใ€— = [(3๐‘ฅ^2)/2+๐‘ฅ]_0^4 = [(3ใ€–(4)ใ€—^2)/2+4โˆ’[(3ใ€–(0)ใ€—^2)/2+0]] = (3 ร— 16)/2 + 4 โˆ’ 0 = 24 + 4 = 28 Area OACD Area OACD = โˆซ1_0^4โ–’ใ€–๐‘ฆ ๐‘‘๐‘ฅใ€— Here, y = 2x + 1 Area OACD = โˆซ1_0^4โ–’ใ€–(2๐‘ฅ+1) ๐‘‘๐‘ฅใ€— = [(2๐‘ฅ^2)/2+๐‘ฅ]_0^4 = [(2ใ€–ร—4ใ€—^2)/2+4โˆ’[(2ใ€– ร— 0ใ€—^2)/2+0]] = 16 + 4 โˆ’ 0 = 20 Area Required = Area ABDO โˆ’ Area ACDO = 28 โˆ’ 20 = 8 square unit

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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.