Evaluate: ∫_(-1)^1 log((2-x)/(2+x))dx

The rest of the post is locked. Join Teachoo Black to see the full post.


This is of the form โˆซ_(โˆ’๐‘Ž)^๐‘Žโ–’๐‘“(๐‘ฅ)๐‘‘๐‘ฅ where ๐’‡(๐’™)=๐ฅ๐จ๐ ((๐Ÿโˆ’๐’™)/(๐Ÿ+๐’™)) And, ๐’‡(โˆ’๐’™)=log((2 โˆ’ (โˆ’๐‘ฅ))/(2 + (โˆ’๐‘ฅ))) ๐‘“(โˆ’๐‘ฅ)=log((2 + ๐‘ฅ)/(2 โˆ’ ๐‘ฅ)) Using log(๐‘Ž/๐‘) = log a โ€“ log b ๐‘“(โˆ’๐‘ฅ)=logโกใ€–(2+๐‘ฅ)โˆ’logโก(2โˆ’๐‘ฅ)ใ€— ๐‘“(โˆ’๐‘ฅ)=ใ€–โˆ’(logใ€—โกใ€–( 2โˆ’๐‘ฅ)โˆ’logโก(2+๐‘ฅ)ใ€—) ๐’‡(โˆ’๐’™)=โˆ’๐ฅ๐จ๐ ((๐Ÿ โˆ’ ๐’™)/(๐Ÿ + ๐’™)) Thus, ๐‘“(โˆ’๐‘ฅ)=โˆ’๐‘“(๐‘ฅ) โˆดโˆซ_(โˆ’1)^1โ€Šlog((2 โˆ’ ๐‘ฅ)/(2 + ๐‘ฅ))๐‘‘๐‘ฅ=0

Go Ad-free
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.