Integration Full Chapter Explained -



  1. Chapter 7 Class 12 Integrals
  2. Concept wise


Ex 7.11, 18 By using the properties of definite integrals, evaluate the integrals : โˆซ_0^4โ–’|๐‘ฅโˆ’1| ๐‘‘๐‘ฅ |๐‘ฅโˆ’1|= {โ–ˆ( (๐‘ฅโˆ’1) ๐‘–๐‘“ ๐‘ฅโˆ’1โ‰ฅ0@โˆ’(๐‘ฅโˆ’1) ๐‘–๐‘“ ๐‘ฅโˆ’1<0)โ”ค = {โ–ˆ((๐‘ฅโˆ’1,) ๐‘–๐‘“ ๐‘ฅโ‰ฅ1@โˆ’(๐‘ฅโˆ’1) ๐‘–๐‘“ ๐‘ฅ<1)โ”ค โˆด โˆซ_0^4โ–’|๐‘ฅโˆ’1|๐‘‘๐‘ฅ=โˆซ_0^1โ–’|๐‘ฅโˆ’1|๐‘‘๐‘ฅ+โˆซ_1^4โ–’|๐‘ฅโˆ’1|๐‘‘๐‘ฅ Using the property, P2 P2 :- โˆซ_๐‘Ž^๐‘โ–’ใ€–๐‘“(๐‘ฅ)๐‘‘๐‘ฅ=ใ€— โˆซ_๐‘Ž^๐‘โ–’ใ€–๐‘“(๐‘ฅ)๐‘‘๐‘ฅ+โˆซ_๐‘^๐‘โ–’๐‘“(๐‘ฅ)๐‘‘๐‘ฅใ€— =โˆซ_0^1โ–’ใ€–โˆ’(๐‘ฅโˆ’1)๐‘‘๐‘ฅ+ใ€— โˆซ_1^4โ–’(๐‘ฅโˆ’1)๐‘‘๐‘ฅ =โˆซ_0^1โ–’ใ€–(โˆ’๐‘ฅ+1)๐‘‘๐‘ฅ+ใ€— โˆซ_1^4โ–’(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+[(16 โˆ’ 1)/2]โˆ’3 =โˆ’1/2+15/2โˆ’3+1 =(14 )/2โˆ’2= 7 โˆ’ 2 = 5

Chapter 7 Class 12 Integrals
Concept wise

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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.