Ex 7.2, 23 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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 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 and Computer Science at Teachoo