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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

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Transcript

Ex 7.4, 3 1/√((2 βˆ’ π‘₯)^2 + 1) Let 2βˆ’π‘₯=𝑑 Diff both sides w.r.t. x 0βˆ’1=𝑑𝑑/𝑑π‘₯ 𝑑π‘₯=βˆ’π‘‘π‘‘ Integrating the function 𝑀.π‘Ÿ.𝑑.π‘₯ ∫1β–’1/√((2 βˆ’ π‘₯)^2 + 1) 𝑑π‘₯ Put the Values of 2βˆ’π‘₯=𝑑 and 𝑑π‘₯=βˆ’π‘‘π‘‘ =∫1β–’(βˆ’π‘‘π‘‘)/√(𝑑^2 + 1) =βˆ’βˆ«1▒𝑑𝑑/√(𝑑^2 +(1)^2 ) =βˆ’log⁑|𝑑+√(𝑑^2+1) |+𝐢 =log⁑〖|𝑑+√(𝑑^2+1) |^(βˆ’1) γ€—+𝐢 =log⁑〖1/|𝑑 + √(𝑑^2 + 1) | γ€— +𝐢 =log⁑〖1/|2 βˆ’ π‘₯ + √((2 βˆ’ π‘₯)^2 + 1) | γ€— +𝐢 =log⁑〖1/|2 βˆ’ π‘₯ + √(γ€–4 + π‘₯γ€—^2 βˆ’ 4π‘₯ + 1) | γ€— +𝐢 =π’π’π’ˆβ‘γ€–πŸ/|𝟐 βˆ’ 𝒙 + √(𝒙^𝟐 βˆ’ πŸ’π’™ + πŸ“) | γ€— +π‘ͺ

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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.