Example 2 - Chapter 7 Class 12 Integrals - Part 4

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

Transcript

Example 2 Find the following integrals: (iii) โˆซโ–’(๐‘ฅ^(3/2)+2๐‘’^๐‘ฅโˆ’1/๐‘ฅ) ๐‘‘๐‘ฅ โˆซ1โ–’(๐‘ฅ^(3/2)+2๐‘’^๐‘ฅโˆ’1/๐‘ฅ) ๐‘‘๐‘ฅ =โˆซ1โ–’๐‘ฅ^(3/2) ๐‘‘๐‘ฅ+2โˆซ1โ–’๐‘’^๐‘ฅ ๐‘‘๐‘ฅโˆ’โˆซ1โ–’1/๐‘ฅ ๐‘‘๐‘ฅ = ๐‘ฅ^(3/2 + 1)/(3/2 + 1) +2๐‘’^๐‘ฅโˆ’logโกใ€– |๐‘ฅ|ใ€—+๐ถ = ๐‘ฅ^(5/2)/(5/2)+2๐‘’^๐‘ฅโˆ’ใ€–log ใ€—โก|๐‘ฅ|+๐ถ = ใ€–๐Ÿ๐’™ ใ€—^(๐Ÿ“/๐Ÿ)/๐Ÿ“+๐Ÿ๐’†^๐’™โˆ’ใ€–๐’๐’๐’ˆ ใ€—โก|๐’™|+๐‘ช As โˆซ1โ–’๐‘ฅ^๐‘› ๐‘‘๐‘ฅ=๐‘ฅ^(๐‘› + 1)/(๐‘› + 1) +๐ถ โˆซ1โ–’๐‘’^๐‘ฅ ๐‘‘๐‘ฅ=๐‘’^๐‘ฅ +๐ถ โˆซ1โ–’1/๐‘ฅ ๐‘‘๐‘ฅ=logโกใ€– |๐‘ฅ|ใ€— +๐ถ

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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.