Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Ex 7.8
Ex 7.8, 2
Ex 7.8, 3
Ex 7.8, 4 Important
Ex 7.8, 5
Ex 7.8, 6
Ex 7.8, 7
Ex 7.8, 8 Important
Ex 7.8, 9
Ex 7.8, 10
Ex 7.8, 11 Important
Ex 7.8, 12
Ex 7.8, 13
Ex 7.8, 14 Important
Ex 7.8, 15 You are here
Ex 7.8, 16 Important
Ex 7.8, 17 Important
Ex 7.8, 18
Ex 7.8, 19 Important
Ex 7.8, 20 Important
Ex 7.8, 21 (MCQ) Important
Ex 7.8, 22 (MCQ)
Last updated at June 13, 2023 by Teachoo
Ex 7.8, 15 โซ_0^1โใ๐ฅ๐^(๐ฅ^2 ) ใ ๐๐ฅ Step 1 :- Let F(๐ฅ)=โซ1โใ๐ฅ๐^(๐ฅ^2 ) ๐๐ฅใ Let ๐ฅ^2=๐ก Differentiating w.r.t. ๐ฅ 2๐ฅ=๐๐ก/๐๐ฅ ๐๐ฅ=๐๐ก/2๐ฅ Therefore, โซ1โใ๐ฅ ๐^(๐ฅ^2 ) ๐๐ฅ=โซ1โใ๐ฅ ๐^๐ก ๐๐ก/2๐ฅใใ =1/2 โซ1โใ๐^๐ก ๐๐กใ =1/2 ๐^๐ก Putting ๐ก=๐ฅ^2 =1/2 ๐^(๐ฅ^2 ) Hence, F(๐ฅ)=1/2 ๐^(๐ฅ^2 ) Step 2 :- โซ_0^1โใ๐ฅ๐^(๐ฅ^2 ) ๐๐ฅใ=๐น(1)โ๐น(0) =1/2 ๐^(1^2 )โ1/2 ๐^(0^2 ) =1/2 ๐^1โ1/2 ๐^0 =๐/๐ (๐โ๐)