Chapter 7 Class 12 Integrals
Concept wise

Example 9 (i) - Example 9Find the following integrals dx / x2 - x6 - Chapter 7 Class 12 CBSE NCERT Math - Integration by specific formulaes - Formula 3

Example 9 (i) - 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 )("Adding and subtracting " (3)^2 ) = โˆซ1โ–’๐‘‘๐‘ฅ/((๐‘ฅ โˆ’ 3)^2 + 13 โˆ’ 9)("Using " ๐‘Ž^2โˆ’2๐‘Ž๐‘+๐‘^2=(๐‘Žโˆ’๐‘)^2 ) = โˆซ1โ–’๐‘‘๐‘ฅ/((๐‘ฅ โˆ’ 3)^2 + 4) = โˆซ1โ–’๐‘‘๐‘ฅ/((๐‘ฅ โˆ’ 3)^2 + 2^2 ) 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

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.