Integration Full Chapter Explained - https://you.tube/Integration-Class-12

Slide52.JPG

Slide53.JPG

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

Transcript

Ex 7.11, 20 The value of โˆซ_((โˆ’ ๐œ‹)/2)^(๐œ‹/2)โ–’ใ€–(๐‘ฅ^3+๐‘ฅ ๐‘๐‘œ๐‘  ๐‘ฅ+tan^5โกใ€–๐‘ฅ+1ใ€— ) ๐‘‘๐‘ฅใ€— (A) 0 (B) 2 (C) ๐œ‹ (D) 1 โˆซ_((โˆ’๐œ‹)/2)^(๐œ‹/2)โ–’ใ€– (๐‘ฅ^3+๐‘ฅ ๐‘๐‘œ๐‘  ๐‘ฅ+tan^5โกใ€–๐‘ฅ+1ใ€— ) ๐‘‘๐‘ฅใ€— We know that โˆซ_(โˆ’๐‘Ž)^(+๐‘Ž)โ–’ใ€–๐‘“(๐‘ฅ) ๐‘‘๐‘ฅใ€—={โ–ˆ(0, ๐‘–๐‘“ ๐‘“(โˆ’๐‘ฅ)=โˆ’๐‘“(๐‘ฅ)@&2โˆซ_0^๐‘Žโ–’ใ€–๐‘“(๐‘ฅ) ๐‘‘๐‘ฅใ€—, ๐‘–๐‘“ ๐‘“(โˆ’๐‘ฅ)=๐‘“(๐‘ฅ) )โ”ค Thus, our equation becomes โˆซ_((โˆ’ ๐œ‹)/2)^(๐œ‹/2)โ–’ใ€–(๐‘ฅ^3+๐‘ฅ ๐‘๐‘œ๐‘  ๐‘ฅ+tan^5โกใ€–๐‘ฅ+1ใ€— ) ๐‘‘๐‘ฅใ€— = โˆซ_0^(๐œ‹/2)โ–’ใ€–0 ๐‘‘๐‘ฅ+โˆซ_0^(๐œ‹/2)โ–’ใ€–0 ๐‘‘๐‘ฅ+โˆซ_0^(๐œ‹/2)โ–’ใ€–0 ๐‘‘๐‘ฅ+๐Ÿโˆซ_๐ŸŽ^(๐…/๐Ÿ)โ–’๐’…๐’™ใ€—ใ€—ใ€— = 2โˆซ_0^(๐œ‹/2)โ–’๐‘‘๐‘ฅ = 2 [๐‘ฅ]_0^(๐œ‹/2) = 2(๐œ‹/2โˆ’0) =๐… Thus, correct option is C

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.