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Ex 7.11, 18 - Evaluate definite integral |x - 1| dx - Ex 7.11

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex 7.11, 18 By using the properties of definite integrals, evaluate the integrals : โˆซ_0^4โ–’|๐‘ฅโˆ’1| ๐‘‘๐‘ฅ =โˆซ_0^1โ–’ใ€–โˆ’๐‘ฅ ๐‘‘๐‘ฅ+ใ€— โˆซ_0^1โ–’ใ€–1. ๐‘‘๐‘ฅ+โˆซ_1^4โ–’ใ€–๐‘ฅ . ๐‘‘๐‘ฅโˆ’โˆซ_1^4โ–’ใ€–1.๐‘‘๐‘ฅใ€—ใ€—ใ€— =โˆ’[๐‘ฅ^2/2]_0^1+[๐‘ฅ]_0^1โˆ’[๐‘ฅ^2/2]_1^4โˆ’[๐‘ฅ]_1^4 =โˆ’[((1)^2 โˆ’ 0)/2]+[1โˆ’0]+[((4)^2โˆ’(1)^2)/2]โˆ’[4โˆ’1] =โˆ’1/2+1+[(16โˆ’1)/2]โˆ’3 =โˆ’1/2+15/2โˆ’3+1 =(14 )/2โˆ’2 = 7 โˆ’ 2 = 5

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