# Ex 7.8, 13 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by Teachoo

Ex 7.8

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Ex 7.8, 13 You are here

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Ex 7.8, 21 (MCQ) Important

Ex 7.8, 22 (MCQ)

Last updated at April 16, 2024 by Teachoo

Ex 7.8, 13 โซ_2^3โ๐ฅ๐๐ฅ/(๐ฅ2+1) Step 1 :- Let F(๐ฅ)=โซ1โใ๐ฅ/(๐ฅ^2 + 1) ๐๐ฅใ Let ๐ฅ^2 + 1=๐ก Differentiating w.r.t.๐ฅ ๐/๐๐ฅ (๐ฅ^2+1)=๐๐ก/๐๐ฅ 2๐ฅ=๐๐ก/๐๐ฅ d๐ฅ=๐๐ก/2๐ฅ Putting Values of ๐ฅ^2+1=๐ก & ๐๐ฅ=๐๐ก/2๐ฅ โซ1โใ(๐ฅ ๐๐ฅ)/(๐ฅ^2 + 1)=โซ1โใ๐ฅ/๐ก ๐๐ก/2๐ฅใใ =1/2 โซ1โ๐๐ก/๐ก =1/2 ๐๐๐|๐ก| =1/2 ๐๐๐|๐ฅ^2+1| Hence F(๐ฅ)=1/2 ๐๐๐|๐ฅ^2+1| Step 2 :- โซ_2^3โ(๐ฅ ๐๐ฅ)/(๐ฅ^2+1)=๐น(3)โ๐น(2) =1/2 ๐๐๐|3^2+1|โ1/2 ๐๐๐|2^2+1| =1/2 logโกใ10โ1/2 ๐๐๐(5)ใ =1/2 (logโกใ10โlogโก5 ใ ) =1/2 ๐๐๐ 10/5 =๐/๐ ๐ฅ๐จ๐ โก๐