Example 8 - Chapter 7 Class 12 Integrals - Part 2

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Example 8 - Chapter 7 Class 12 Integrals - Part 3

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  1. Chapter 7 Class 12 Integrals (Term 2)
  2. Serial order wise

Transcript

Example 8 Find the following integrals: (ii) โˆซ1โ–’๐‘‘๐‘ฅ/โˆš(2๐‘ฅ โˆ’ ๐‘ฅ^2 ) โˆซ1โ–’๐‘‘๐‘ฅ/โˆš(2๐‘ฅ โˆ’ ๐‘ฅ^2 ) Adding and subtracting 1 in denominator = โˆซ1โ–’๐‘‘๐‘ฅ/โˆš(โˆ’ใ€– ๐‘ฅใ€—^2 + 2๐‘ฅ + 1โˆ’1) = โˆซ1โ–’๐‘‘๐‘ฅ/โˆš(1 โˆ’ ๐‘ฅ^2 + 2๐‘ฅ โˆ’ 1) = โˆซ1โ–’๐‘‘๐‘ฅ/โˆš(1 โˆ’ (๐‘ฅ^2 โˆ’ 2๐‘ฅ + 1) ) = โˆซ1โ–’๐‘‘๐‘ฅ/โˆš(1 โˆ’ใ€– (๐‘ฅ โˆ’ 1)ใ€—^2 ) = โˆซ1โ–’๐‘‘๐‘ฅ/โˆš(1^2 โˆ’ใ€– (๐‘ฅ โˆ’ 1)ใ€—^2 ) =sin^(โˆ’1)โกใ€–(๐‘ฅ โˆ’ 1)/1+Cใ€— =ใ€–๐’”๐’Š๐’ใ€—^(โˆ’๐Ÿ)โกใ€–(๐’™โˆ’๐Ÿ)+๐‘ชใ€— It is of the form ๐‘‘๐‘ฅ/โˆš(๐‘Ž^2 โˆ’ ๐‘ฅ^2 )=sin^(โˆ’1) ๐‘ฅ/๐‘Ž+๐ถ Replacing a with 1 and ๐‘ฅ with ๐‘ฅโˆ’1

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.