Ex 7.11, 17 - Evaluate root x / root x + root a - x dx - Ex 7.11

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

Transcript

Ex 7.11, 17 By using the properties of definite integrals, evaluate the integrals : โˆซ_0^๐‘Žโ–’โˆš๐‘ฅ/(โˆš๐‘ฅ + โˆš(๐‘Ž โˆ’ ๐‘ฅ)) ๐‘‘๐‘ฅ Let I=โˆซ_0^๐‘Žโ–’โˆš๐‘ฅ/(โˆš๐‘ฅ + โˆš(๐‘Ž โˆ’ ๐‘ฅ)) ๐‘‘๐‘ฅ โˆด I=โˆซ_0^๐‘Žโ–’ใ€–โˆš(๐‘Ž โˆ’ ๐‘ฅ)/(โˆš(๐‘Ž โˆ’ ๐‘ฅ) +โˆš(๐‘Ž โˆ’ (๐‘Ž โˆ’ ๐‘ฅ) )) ๐‘‘๐‘ฅใ€— I= โˆซ_0^๐‘Žโ–’ใ€–โˆš(๐‘Ž โˆ’ ๐‘ฅ)/(โˆš(๐‘Ž โˆ’ ๐‘ฅ) + โˆš(๐‘Ž โˆ’ ๐‘Ž + ๐‘ฅ)) ๐‘‘๐‘ฅใ€— I=โˆซ_0^๐‘Žโ–’ใ€–โˆš(๐‘Ž โˆ’ ๐‘ฅ)/(โˆš(๐‘Ž โˆ’ ๐‘ฅ) + โˆš๐‘ฅ) ๐‘‘๐‘ฅใ€— Adding (1) and (2) i.e (1) + (2) I + I = โˆซ_0^๐‘Žโ–’ใ€–โˆš๐‘ฅ/(โˆš๐‘ฅ +โˆš(๐‘Ž โˆ’ ๐‘ฅ)) ๐‘‘๐‘ฅใ€—+โˆซ_0^๐‘Žโ–’ใ€–โˆš(๐‘Ž โˆ’ ๐‘ฅ)/(โˆš(๐‘Žโˆ’ ๐‘ฅ) + โˆš( ๐‘ฅ)) ๐‘‘๐‘ฅใ€— 2I = โˆซ_0^๐‘Žโ–’ใ€–(โˆš๐‘ฅ + โˆš(๐‘Ž โˆ’ ๐‘ฅ))/(โˆš๐‘ฅ + โˆš(๐‘Ž โˆ’ ๐‘ฅ)) ๐‘‘๐‘ฅใ€— 2I =โˆซ_0^๐‘Žโ–’ใ€–1.๐‘‘๐‘ฅใ€— 2I = [๐‘ฅ]_0^๐‘Ž 2I = [๐‘Žโˆ’0] ๐ˆ =๐’‚/๐Ÿ

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.