Ex 7.2, 23 sin^(−1)⁡𝑥/√(1 − 𝑥^2 ) Step 1: Let sin^(−1)⁡𝑥=𝑡 Differentiating both sides 𝑤.𝑟.𝑡.𝑥 1/√(1 − 𝑥^2 )= 𝑑𝑡/𝑑𝑥 𝑑𝑥=√(1 − 𝑥^2 ) .𝑑𝑡 Step 2: Integrating the function ∫1▒〖" " sin^(−1)⁡𝑥/√(1 − 𝑥^2 ) " " 〗. 𝑑𝑥 putting sin^(−1)⁡𝑥=𝑡 & 𝑑𝑥=√(1 − 𝑥^2 ) .𝑑𝑡 = ∫1▒〖𝑡/√(1 − 𝑥^2 ) " " 〗. √(1 − 𝑥^2 ) .𝑑𝑡 = ∫1▒〖𝑡 . 𝑑𝑡〗 = 𝑡^2/2+𝐶 = (〖𝒔𝒊𝒏〗^(−𝟏)⁡𝒙 )^𝟐/𝟐+𝑪

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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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