Ex 7.8, 9 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by

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Transcript

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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