CBSE Class 12 Sample Paper for 2023 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## (d) logโก9/4

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This question is Similar to Ex - 7.10 -1

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Question 9 The value of "โซ" _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 โซ_๐^๐โใ๐/(๐^๐ + ๐) ๐๐ใ Let ๐=๐^๐+๐ 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๐=๐๐ Now, when ๐ varies from 2 to 3 then ๐ varies from 5 to 10 Therefore โซ_๐^๐โใ๐/(๐^๐+๐) ๐๐=โซ_๐^๐๐โใ๐/๐ ๐๐/๐๐ใใ =1/2 โซ_5^10โ๐๐ก/๐ก =๐/๐ [๐๐๐|๐|]_๐^๐๐ =1/2 [๐๐๐|10|โ๐๐๐|5|] =1/2 [๐๐๐|10/5|] =1/2 ๐๐๐|2| =๐/๐ ๐๐๐ ๐So, the correct answer is (c)