Integration Full Chapter Explained - Integration Class 12 - Everything you need



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


Ex 7.3, 13 Integrate the function cosโกใ€–2๐‘ฅ โˆ’ cosโก2๐›ผ ใ€—/cosโกใ€–๐‘ฅ โˆ’ cosโก๐›ผ ใ€— โˆซ1โ–’ใ€–cosโกใ€–2๐‘ฅ โˆ’ cosโก2๐›ผ ใ€—/cosโกใ€–๐‘ฅ โˆ’ cosโก๐›ผ ใ€— " " ๐‘‘๐‘ฅใ€— =โˆซ1โ–’((2 cos^2โกใ€–๐‘ฅ โˆ’ 1ใ€— ) โˆ’ (2 cos^2โกใ€–๐›ผ โˆ’ 1ใ€— ))/(cosโก๐‘ฅ โˆ’ cosโก๐›ผ ) ๐‘‘๐‘ฅ =โˆซ1โ–’(2 cos^2โกใ€–๐‘ฅ โˆ’ 1ใ€— โˆ’ 2 cos^2โกใ€–๐›ผ + 1ใ€—)/(cosโก๐‘ฅ โˆ’ cosโก๐›ผ ) ๐‘‘๐‘ฅ =โˆซ1โ–’(2 cos^2โก๐‘ฅ โˆ’ 2 cos^2โก๐›ผ + 1 โˆ’ 1)/(cosโก๐‘ฅ โˆ’ cosโก๐›ผ ) ๐‘‘๐‘ฅ =โˆซ1โ–’2(cos^2โก๐‘ฅ โˆ’ cos^2โก๐›ผ )/(cosโก๐‘ฅ โˆ’ cosโก๐›ผ ) ๐‘‘๐‘ฅ =2โˆซ1โ–’(cos^2โก๐‘ฅ โˆ’ cos^2โก๐›ผ)/(cosโก๐‘ฅ โˆ’ cosโก๐›ผ ) ๐‘‘๐‘ฅ =2โˆซ1โ–’((๐‘๐‘œ๐‘ โก๐‘ฅ โˆ’ ๐‘๐‘œ๐‘ โก๐›ผ ) (๐‘๐‘œ๐‘ โก๐‘ฅ + ๐‘๐‘œ๐‘ โก๐›ผ ))/((๐‘๐‘œ๐‘ โก๐‘ฅ โˆ’ ๐‘๐‘œ๐‘ โก๐›ผ ) ) ๐‘‘๐‘ฅ =2โˆซ1โ–’(๐‘๐‘œ๐‘ โก๐‘ฅ+๐‘๐‘œ๐‘ โก๐›ผ ) ๐‘‘๐‘ฅ =2(โˆซ1โ–’๐‘๐‘œ๐‘ โก๐‘ฅ ๐‘‘๐‘ฅ+โˆซ1โ–’๐‘๐‘œ๐‘ โก๐›ผ ๐‘‘๐‘ฅ) =2(โˆซ1โ–’๐‘๐‘œ๐‘ โก๐‘ฅ ๐‘‘๐‘ฅ+๐‘๐‘œ๐‘ โก๐›ผ โˆซ1โ–’1. ๐‘‘๐‘ฅ) =๐Ÿ(๐’”๐’Š๐’โก๐’™+๐’™โก๐’„๐’๐’” ๐œถ)" +" ๐‘ช (๐‘๐‘œ๐‘ โก2๐œƒ=2 ใ€–๐‘๐‘œ๐‘ ใ€—^2โก๐œƒโˆ’1)

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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.