# Ex 7.8, 15 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by Teachoo

Ex 7.8

Ex 7.8, 1

Ex 7.8, 2

Ex 7.8, 3

Ex 7.8, 4 Important

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Ex 7.8, 8 Important

Ex 7.8, 9

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Ex 7.8, 11 Important

Ex 7.8, 12

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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 April 16, 2024 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)