The value of ∫ 2 3 x/x 2 +1 dx is

(a) log⁡4     

(b) log⁡3/2   

(c) 1/2  log⁡2  

(d) log⁡9/4

 

This question is Similar to Ex - 7.10 -1

 

Slide17.JPG

Slide18.JPG
Slide19.JPG

 

This video is only available for Teachoo black users

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 9 The value of "โˆซ" _2^3 ๐‘ฅ/(๐‘ฅ^2+1) ๐‘‘๐‘ฅ is (a) logโก4 (b) logโกใ€–3/2ใ€— (c) 1/2 logโก2 (d) logโกใ€–9/4ใ€—We need to find โˆซ_๐Ÿ^๐Ÿ‘โ–’ใ€–๐’™/(๐’™^๐Ÿ + ๐Ÿ) ๐’…๐’™ใ€— Let ๐’•=๐’™^๐Ÿ+๐Ÿ Differentiating w.r.t. ๐‘ฅ ๐‘‘๐‘ก/๐‘‘๐‘ฅ=๐‘‘/๐‘‘๐‘ฅ (๐‘ฅ^2+1) ๐‘‘๐‘ก/๐‘‘๐‘ฅ=2๐‘ฅ ๐’…๐’•/๐Ÿ๐’™=๐’…๐’™ Now, when ๐’™ varies from 2 to 3 then ๐’• varies from 5 to 10 Therefore โˆซ_๐Ÿ^๐Ÿ‘โ–’ใ€–๐’™/(๐’™^๐Ÿ+๐Ÿ) ๐’…๐’™=โˆซ_๐Ÿ“^๐Ÿ๐ŸŽโ–’ใ€–๐’™/๐’• ๐’…๐’•/๐Ÿ๐’™ใ€—ใ€— =1/2 โˆซ_5^10โ–’๐‘‘๐‘ก/๐‘ก =๐Ÿ/๐Ÿ [๐’๐’๐’ˆ|๐’•|]_๐Ÿ“^๐Ÿ๐ŸŽ =1/2 [๐‘™๐‘œ๐‘”|10|โˆ’๐‘™๐‘œ๐‘”|5|] =1/2 [๐‘™๐‘œ๐‘”|10/5|] =1/2 ๐‘™๐‘œ๐‘”|2| =๐Ÿ/๐Ÿ ๐’๐’๐’ˆ ๐ŸSo, the correct answer is (c)

Ask a doubt
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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.