Ex 7.4, 3 - Integrate 1 / root (2 - x)2 + 1 - Class 12 - Integration by specific formulaes - Formula 6

Ex 7.4, 3 - Chapter 7 Class 12 Integrals - Part 2


Transcript

Ex 7.4, 3 1/โˆš((2 โˆ’ ๐‘ฅ)^2 + 1) Let 2โˆ’๐‘ฅ=๐‘ก Diff both sides w.r.t. x 0โˆ’1=๐‘‘๐‘ก/๐‘‘๐‘ฅ ๐‘‘๐‘ฅ=โˆ’๐‘‘๐‘ก Integrating the function ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ โˆซ1โ–’1/โˆš((2 โˆ’ ๐‘ฅ)^2 + 1) ๐‘‘๐‘ฅ Put the Values of 2โˆ’๐‘ฅ=๐‘ก and ๐‘‘๐‘ฅ=โˆ’๐‘‘๐‘ก =โˆซ1โ–’(โˆ’๐‘‘๐‘ก)/โˆš(๐‘ก^2 + 1) =โˆ’โˆซ1โ–’๐‘‘๐‘ก/โˆš(๐‘ก^2 +(1)^2 ) =โˆ’logโก|๐‘ก+โˆš(๐‘ก^2+1) |+๐ถ =logโกใ€–|๐‘ก+โˆš(๐‘ก^2+1) |^(โˆ’1) ใ€—+๐ถ =logโกใ€–1/|๐‘ก + โˆš(๐‘ก^2 + 1) | ใ€— +๐ถ =logโกใ€–1/|2 โˆ’ ๐‘ฅ + โˆš((2 โˆ’ ๐‘ฅ)^2 + 1) | ใ€— +๐ถ =logโกใ€–1/|2 โˆ’ ๐‘ฅ + โˆš(ใ€–4 + ๐‘ฅใ€—^2 โˆ’ 4๐‘ฅ + 1) | ใ€— +๐ถ =๐’๐’๐’ˆโกใ€–๐Ÿ/|๐Ÿ โˆ’ ๐’™ + โˆš(๐’™^๐Ÿ โˆ’ ๐Ÿ’๐’™ + 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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.