Example 9 - Find integrals (i) dx / x2 - 6x + 13 - Class 12

Example 9 - Chapter 7 Class 12 Integrals - Part 2

 

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Transcript

Example 9 Find the following integrals: (i) โˆซ1โ–’๐‘‘๐‘ฅ/(๐‘ฅ^2โˆ’ 6๐‘ฅ + 13) โˆซ1โ–’๐‘‘๐‘ฅ/(๐‘ฅ^2โˆ’ 6๐‘ฅ + 13) =โˆซ1โ–’๐‘‘๐‘ฅ/(๐‘ฅ^2โˆ’ 2 ร— 3 ร— ๐‘ฅ + 13) = โˆซ1โ–’๐‘‘๐‘ฅ/((๐‘ฅ^2 โˆ’ 2 . 3 ๐‘ฅ + 3^2 ) + 13 โˆ’ 3^2 ) = โˆซ1โ–’๐‘‘๐‘ฅ/((๐‘ฅ โˆ’ 3)^2 + 13 โˆ’ 9) = โˆซ1โ–’๐‘‘๐‘ฅ/((๐‘ฅ โˆ’ 3)^2 + 4) = โˆซ1โ–’๐‘‘๐‘ฅ/((๐‘ฅ โˆ’ 3)^2 + 2^2 ) ("Adding and subtracting " (3)^2 ) ("Using " ๐‘Ž^2โˆ’2๐‘Ž๐‘+๐‘^2=(๐‘Žโˆ’๐‘)^2 ) It is of form ๐‘‘๐‘ฅ/(๐‘ฅ^2 + ๐‘Ž^2 )=1/๐‘Ž ใ€–๐‘ก๐‘Ž๐‘›ใ€—^(โˆ’1)โกใ€–๐‘ฅ/๐‘Žใ€—+๐ถ Replacing ๐‘ฅ with (๐‘ฅโˆ’3) and ๐‘Ž with 2 =๐Ÿ/๐Ÿ ใ€–๐’•๐’‚๐’ใ€—^(โˆ’๐Ÿ)โกใ€–(๐’™ โˆ’ ๐Ÿ‘)/๐Ÿใ€— +๐‘ช

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.