Ex 7.4, 6 - Integrate x2 / 1 - x6 - Chapter 7 CBSE NCERT - Ex 7.4

Slide17.JPG

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

Transcript

Ex 7.4, 6 ๐‘ฅ2/(1 โˆ’ ๐‘ฅ6) Let ๐‘ฅ^3=๐‘ก Diff both sides w.r.t. x 3๐‘ฅ^2=๐‘‘๐‘ก/๐‘‘๐‘ฅ ๐‘‘๐‘ฅ=๐‘‘๐‘ก/(3๐‘ฅ^2 ) Integrating the function ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ โˆซ1โ–’๐‘ฅ^2/(1 โˆ’ ๐‘ฅ^6 ) ๐‘‘๐‘ฅ =โˆซ1โ–’๐‘ฅ^2/(1 โˆ’ (๐‘ฅ^3 )^2 ) ๐‘‘๐‘ฅ Put the values of ๐‘ฅ^3=๐‘ก and ๐‘‘๐‘ฅ=๐‘‘๐‘ก/(3๐‘ฅ^2 ) =โˆซ1โ–’๐‘ฅ^2/(1 โˆ’ ๐‘ก^2 ) . ๐‘‘๐‘ฅ =โˆซ1โ–’๐‘ฅ^2/(1 โˆ’ ๐‘ก^2 ) ร— ๐‘‘๐‘ก/(3๐‘ฅ^2 ) =1/3 โˆซ1โ–’๐‘‘๐‘ก/(1 โˆ’ ๐‘ก^2 ) =1/3 โˆซ1โ–’๐‘‘๐‘ก/((1)^2 โˆ’ ๐‘ก^2 ) =1/3 [1/2(1) logโก|(1 + ๐‘ก)/(1 โˆ’ ๐‘ก)| ]+๐ถ =1/6 logโก|(1 + ๐‘ก)/(1 โˆ’ ๐‘ก)|+๐ถ =๐Ÿ/๐Ÿ” ๐’๐’๐’ˆโก|(๐Ÿ + ๐’™^๐Ÿ‘)/(๐Ÿ โˆ’ ๐’™^๐Ÿ‘ )|+๐‘ช

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 provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail