Ex 7.2, 23 - Integrate sin-1 x / root(1 - x2) - Class 12 - Integration by substitution - Trignometric - Inverse

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  1. Chapter 7 Class 12 Integrals
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Ex 7.2, 23 sin^(โˆ’1)โก๐‘ฅ/โˆš(1 โˆ’ ๐‘ฅ^2 ) Step 1: Let sin^(โˆ’1)โก๐‘ฅ=๐‘ก Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ 1/โˆš(1 โˆ’ ๐‘ฅ^2 )= ๐‘‘๐‘ก/๐‘‘๐‘ฅ ๐‘‘๐‘ฅ=โˆš(1 โˆ’ ๐‘ฅ^2 ) .๐‘‘๐‘ก Step 2: Integrating the function โˆซ1โ–’ใ€–" " sin^(โˆ’1)โก๐‘ฅ/โˆš(1 โˆ’ ๐‘ฅ^2 ) " " ใ€—. ๐‘‘๐‘ฅ putting sin^(โˆ’1)โก๐‘ฅ=๐‘ก & ๐‘‘๐‘ฅ=โˆš(1 โˆ’ ๐‘ฅ^2 ) .๐‘‘๐‘ก = โˆซ1โ–’ใ€–๐‘ก/โˆš(1 โˆ’ ๐‘ฅ^2 ) " " ใ€—. โˆš(1 โˆ’ ๐‘ฅ^2 ) .๐‘‘๐‘ก = โˆซ1โ–’ใ€–๐‘ก . ๐‘‘๐‘กใ€— = ๐‘ก^2/2+๐ถ = (ใ€–๐’”๐’Š๐’ใ€—^(โˆ’๐Ÿ)โก๐’™ )^๐Ÿ/๐Ÿ+๐‘ช

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