Chapter 7 Class 12 Integrals
Concept wise

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Transcript

Ex 7.8, 15 โˆซ_0^1โ–’ใ€–๐‘ฅ๐‘’^(๐‘ฅ^2 ) ใ€— ๐‘‘๐‘ฅ Step 1 :- Let F(๐‘ฅ)=โˆซ1โ–’ใ€–๐‘ฅ๐‘’^(๐‘ฅ^2 ) ๐‘‘๐‘ฅใ€— Let ๐‘ฅ^2=๐‘ก Differentiating w.r.t. ๐‘ฅ 2๐‘ฅ=๐‘‘๐‘ก/๐‘‘๐‘ฅ ๐‘‘๐‘ฅ=๐‘‘๐‘ก/2๐‘ฅ Therefore, โˆซ1โ–’ใ€–๐‘ฅ ๐‘’^(๐‘ฅ^2 ) ๐‘‘๐‘ฅ=โˆซ1โ–’ใ€–๐‘ฅ ๐‘’^๐‘ก ๐‘‘๐‘ก/2๐‘ฅใ€—ใ€— =1/2 โˆซ1โ–’ใ€–๐‘’^๐‘ก ๐‘‘๐‘กใ€— =1/2 ๐‘’^๐‘ก Putting ๐‘ก=๐‘ฅ^2 =1/2 ๐‘’^(๐‘ฅ^2 ) Hence, F(๐‘ฅ)=1/2 ๐‘’^(๐‘ฅ^2 ) Step 2 :- โˆซ_0^1โ–’ใ€–๐‘ฅ๐‘’^(๐‘ฅ^2 ) ๐‘‘๐‘ฅใ€—=๐น(1)โˆ’๐น(0) =1/2 ๐‘’^(1^2 )โˆ’1/2 ๐‘’^(0^2 ) =1/2 ๐‘’^1โˆ’1/2 ๐‘’^0 =๐Ÿ/๐Ÿ (๐’†โˆ’๐Ÿ)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.