CBSE Class 12 Sample Paper for 2023 Boards

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Question 9 - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by

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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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)

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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 and Computer Science at Teachoo