1. Chapter 7 Class 12 Integrals
  2. Serial order wise
  3. Ex 7.6
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Ex 7.6, 20 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by Teachoo

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Ex 7.6, 20 Integrate the function (๐‘ฅ โˆ’ 3)๐‘’๐‘ฅ/(๐‘ฅ โˆ’ 1)3 โˆซ1โ–’ใ€–((๐‘ฅ โˆ’ 3))/(๐‘ฅ โˆ’1)3 .๐‘’๐‘ฅ" " ๐‘‘๐‘ฅใ€— = โˆซ1โ–’ใ€–(๐‘ฅ โˆ’ 1 โˆ’ 2)/(๐‘ฅ โˆ’1)^3 .๐‘’๐‘ฅ" " ๐‘‘๐‘ฅใ€— = โˆซ1โ–’ใ€–๐‘’๐‘ฅ ((๐‘ฅ โˆ’ 1)/(๐‘ฅ โˆ’1)^3 โˆ’ 2/(๐‘ฅ โˆ’1)^3 )๐‘‘๐‘ฅใ€— = โˆซ1โ–’ใ€–๐‘’๐‘ฅ (1/(๐‘ฅ โˆ’1)^2 โˆ’ 2/(๐‘ฅ โˆ’1)^3 )๐‘‘๐‘ฅใ€— It is of the form โˆซ1โ–’ใ€–๐‘’^๐‘ฅ [๐‘“(๐‘ฅ)+๐‘“^โ€ฒ (๐‘ฅ)] ใ€— ๐‘‘๐‘ฅ=๐‘’^๐‘ฅ ๐‘“(๐‘ฅ)+๐ถ Where ๐‘“(๐‘ฅ)=" " 1/(๐‘ฅ โˆ’1)^2 โˆด ๐‘“^โ€ฒ (๐‘ฅ)= (โˆ’ 2)/(๐‘ฅ โˆ’ 1)^3 So, our equation becomes โˆซ1โ–’ใ€–๐‘’๐‘ฅ (1/(๐‘ฅ โˆ’ 1)^2 โˆ’ 2/(๐‘ฅ โˆ’ 1)^3 )๐‘‘๐‘ฅใ€— = ๐’†๐’™/(๐’™ โˆ’ ๐Ÿ)๐Ÿ +๐‘ช
  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

    3. Ex 7.6

    Ex 7.7 →
Ex 7.7 →
Chapter 7 Class 12 Integrals
Serial order wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo