Example 8 (ii) - Chapter 7 Class 12 Integrals
Last updated at April 16, 2024 by Teachoo
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Question 3 (Supplementary NCERT) Important Deleted for CBSE Board 2024 Exams
Chapter 7 Class 12 Integrals
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Transcript
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
