Ex 7.8, 9 - Chapter 7 Class 12 Integrals

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Ex 7.8, 9 โˆซ_0^1โ–’๐‘‘๐‘ฅ/โˆš(1โˆ’๐‘ฅ2) Step 1 :- Let F(๐‘ฅ)=โˆซ1โ–’๐‘‘๐‘ฅ/โˆš(1 โˆ’ ๐‘ฅ^2 ) =โˆซ1โ–’๐‘‘๐‘ฅ/โˆš(1^2 โˆ’ ๐‘ฅ^2 ) =sin^(โˆ’1)โกใ€–๐‘ฅ/1ใ€— =๐‘ ๐‘–๐‘›^(โˆ’1) ๐‘ฅ Hence F(๐‘ฅ)=๐‘ ๐‘–๐‘›^(โˆ’1) ๐‘ฅ Step 2 :- โˆซ_0^1โ–’ใ€–๐‘‘๐‘ฅ/โˆš(1 โˆ’ ๐‘ฅ^2 )=๐น(1)โˆ’๐น(0) ใ€— =๐‘ ๐‘–๐‘›^(โˆ’1) (1)โˆ’๐‘ ๐‘–๐‘›^(โˆ’1) (0) =๐œ‹/2โˆ’0 =๐œ‹/2

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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