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Last updated at Dec. 6, 2019 by Teachoo

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Ex7.9, 22 Choose the correct answer โซ_0^(2/3)โ๐๐ฅ/(4 +9๐ฅ^2 ) equals (A) ๐/6 (B) ๐/12 (C) ๐/24 (D) ๐/4 Step 1 :- Let F(๐ฅ)=โซ1โ๐๐ฅ/(4 + 9๐ฅ^2 ) Divide and multiply the integrate by 4 =โซ1โโ(๐๐ฅ@4)/((4 + 9๐ฅ^2)/4) =1/4 โซ1โ๐๐ฅ/(1 + 9/4 ๐ฅ^2 ) =1/4 โซ1โ๐๐ฅ/(1 + (3/2 ๐ฅ)^2 ) Put 3/2 ๐ฅ=๐ก Differentiating w.r.t.๐ฅ ๐(3/2 ๐ฅ)/๐๐ฅ=๐๐ก/๐๐ฅ 3/2=๐๐ก/๐๐ฅ ๐๐ฅ=๐๐ก/(3/2) ๐๐ฅ=2/3 ๐๐ก Hence 1/4 โซ1โใ๐๐ฅ/(1+(3/2 ๐ฅ)^2 )=1/4 โซ1โใ1/(1+๐ก^2 ) 2/3ใ ๐๐กใ =1/4 ร 2/3 โซ1โ๐๐ก/(1+๐ก^2 ) =1/6 tan^(โ1)โก๐ก Putting ๐ก=3/2 ๐ฅ =1/6 tan^(โ1)โกใ3/2 ๐ฅใ Hence F(๐ฅ)=1/6 tan^(โ1)โกใ3/2 ๐ฅใ Step 2 :- โซ_0^(2/3)โใ๐๐ฅ/(4+9๐ฅ^2 )=๐น(2/3)โ๐น(0) ใ =1/6 tan^(โ1)โกใ(3/2 ร 2/3)โ1/6 tan^(โ1)โก(0) ใ =1/6 tan^(โ1)โกใ(1)โ1/6 tan^(โ1)โก(0) ใ =1/6 ร ๐/4โ0 =๐/24 โต Option (C) is correct.

Ex 7.9

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Ex 7.9, 22 You are here

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.