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





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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)

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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.