Ex 7.4, 3 1/√((2 − 𝑥)^2 + 1) Let 2−𝑥=𝑡 Diff both sides w.r.t. x 0−1=𝑑𝑡/𝑑𝑥 𝑑𝑥=−𝑑𝑡 Integrating the function 𝑤.𝑟.𝑡.𝑥 ∫1▒1/√((2 − 𝑥)^2 + 1) 𝑑𝑥 Put the Values of 2−𝑥=𝑡 and 𝑑𝑥=−𝑑𝑡 =∫1▒(−𝑑𝑡)/√(𝑡^2 + 1) =−∫1▒𝑑𝑡/√(𝑡^2 +(1)^2 ) =−log⁡|𝑡+√(𝑡^2+1) |+𝐶 =log⁡〖|𝑡+√(𝑡^2+1) |^(−1) 〗+𝐶 =log⁡〖1/|𝑡 + √(𝑡^2 + 1) | 〗 +𝐶 =log⁡〖1/|2 − 𝑥 + √((2 − 𝑥)^2 + 1) | 〗 +𝐶 =log⁡〖1/|2 − 𝑥 + √(〖4 + 𝑥〗^2 − 4𝑥 + 1) | 〗 +𝐶 =𝒍𝒐𝒈⁡〖𝟏/|𝟐 − 𝒙 + √(𝒙^𝟐 − 𝟒𝒙 + 𝟓) | 〗 +𝑪

Next: Ex 7.4, 4 → Ask a doubt

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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