Example 8 (ii) - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 8 Find the following integrals: (ii) ∫1▒𝑑𝑥/√(2𝑥 − 𝑥^2 ) ∫1▒𝑑𝑥/√(2𝑥 − 𝑥^2 ) Adding and subtracting 1 in denominator = ∫1▒𝑑𝑥/√(−〖 𝑥〗^2 + 2𝑥 + 1−1) = ∫1▒𝑑𝑥/√(1 − 𝑥^2 + 2𝑥 − 1) = ∫1▒𝑑𝑥/√(1 − (𝑥^2 − 2𝑥 + 1) ) = ∫1▒𝑑𝑥/√(1 −〖 (𝑥 − 1)〗^2 ) = ∫1▒𝑑𝑥/√(1^2 −〖 (𝑥 − 1)〗^2 ) =sin^(−1)〖(𝑥 − 1)/1+C〗 =〖𝒔𝒊𝒏〗^(−𝟏)〖(𝒙−𝟏)+𝑪〗 It is of the form 𝑑𝑥/√(𝑎^2 − 𝑥^2 )=sin^(−1) 𝑥/𝑎+𝐶 Replacing a with 1 and 𝑥 with 𝑥−1
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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