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  1. Chapter 7 Class 12 Integrals (Term 2)
  2. Concept wise

Transcript

Ex 7.10, 1 Evaluate the integrals using substitution โˆซ_0^1โ–’ใ€–๐‘ฅ/(๐‘ฅ^2 + 1) ๐‘‘๐‘ฅใ€— We need to find โˆซ_๐ŸŽ^๐Ÿโ–’ใ€–๐’™/(๐’™^๐Ÿ + ๐Ÿ) ๐’…๐’™ใ€— Let ๐’•=๐’™^๐Ÿ+๐Ÿ Differentiating w.r.t. ๐‘ฅ ๐‘‘๐‘ก/๐‘‘๐‘ฅ=๐‘‘/๐‘‘๐‘ฅ (๐‘ฅ^2+1) ๐‘‘๐‘ก/๐‘‘๐‘ฅ=2๐‘ฅ ๐’…๐’•/๐Ÿ๐’™=๐’…๐’™ Now, when ๐’™ varies from 0 to 1 then ๐’• varies from 1 to 2 Therefore โˆซ_๐ŸŽ^๐Ÿโ–’ใ€–๐’™/(๐’™^๐Ÿ+๐Ÿ) ๐’…๐’™=โˆซ_๐Ÿ^๐Ÿโ–’ใ€–๐’™/๐’• ๐’…๐’•/๐Ÿ๐’™ใ€—ใ€— =1/2 โˆซ_1^2โ–’๐‘‘๐‘ก/๐‘ก =๐Ÿ/๐Ÿ [๐’๐’๐’ˆ|๐’•|]_๐Ÿ^๐Ÿ =1/2 [๐‘™๐‘œ๐‘”|2|โˆ’๐‘™๐‘œ๐‘”|1|] =1/2 [๐‘™๐‘œ๐‘”|2|โˆ’0] =1/2 ๐‘™๐‘œ๐‘”|2| =๐Ÿ/๐Ÿ ๐’๐’๐’ˆ ๐Ÿ

Chapter 7 Class 12 Integrals (Term 2)
Concept wise

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.