Ex 7.2, 23 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by

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

Ex 7.2, 23 - Chapter 7 Class 12 Integrals - Part 2

Transcript

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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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.