Integration Full Chapter Explained - https://you.tube/Integration-Class-12

Last updated at Dec. 6, 2019 by Teachoo

Transcript

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

Ex 7.9, 1

Ex 7.9, 2

Ex 7.9, 3

Ex 7.9, 4

Ex 7.9, 5

Ex 7.9, 6

Ex 7.9, 7

Ex 7.9, 8 Important

Ex 7.9, 9

Ex 7.9, 10

Ex 7.9, 11

Ex 7.9, 12

Ex 7.9, 13

Ex 7.9, 14

Ex 7.9, 15

Ex 7.9, 16 Important

Ex 7.9, 17 Important

Ex 7.9, 18

Ex 7.9, 19 Important

Ex 7.9, 20 Important

Ex 7.9, 21 Important

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.