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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

Transcript

Example 38 Evaluate โˆซ1โ–’(๐‘ฅ^4 โˆ’๐‘ฅ)^(1/4)/๐‘ฅ^5 ๐‘‘๐‘ฅ โˆซ1โ–’(๐‘ฅ^4 โˆ’ ๐‘ฅ)^(1/4)/๐‘ฅ^5 ๐‘‘๐‘ฅ Taking ๐‘ฅ^4 common from numerator =โˆซ1โ–’ใ€–(๐‘ฅ^4 )^(1/4) (1 โˆ’ ๐‘ฅ/๐‘ฅ^4 )ใ€—^(1/4)/๐‘ฅ^5 ๐‘‘๐‘ฅ = โˆซ1โ–’(๐‘ฅ (1 โˆ’ 1/๐‘ฅ^3 )^(1/4))/๐‘ฅ^5 ๐‘‘๐‘ฅ = โˆซ1โ–’(1 โˆ’ 1/๐‘ฅ^3 )^(1/4)/๐‘ฅ^4 ๐‘‘๐‘ฅ Let t = 1 โˆ’ 1/๐‘ฅ^3 ๐‘‘๐‘ก/๐‘‘๐‘ฅ=3/๐‘ฅ^4 Substituting values, =โˆซ1โ–’ใ€–๐‘ก ใ€—^(1/4)/3 ๐‘‘๐‘ก = 1/3 (((๐‘ก^( 1/(4 ) + 1) ))/(1/4 +1))+ C = 1/3 ((๐‘ก^( 5/4) )/(5/4))+ C = 4/15 ใ€–๐‘ก ใ€—^(5/4)+ C = ๐Ÿ’/๐Ÿ๐Ÿ“ (๐Ÿโˆ’๐Ÿ/๐’™^๐Ÿ‘ )^( ๐Ÿ“/๐Ÿ’)+ C

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.