Example 8 - Chapter 7 Class 12 Integrals - Part 2

Example 8 - Chapter 7 Class 12 Integrals - Part 3


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 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, Social Science, Physics, Chemistry, Computer Science at Teachoo.