Integration Full Chapter Explained - Integration Class 12 - Everything you need


Last updated at Dec. 20, 2019 by Teachoo
Transcript
Ex 7.2, 19 Integrate the function (๐2๐ฅ โ 1)/(๐2๐ฅ+ 1) Simplify the given function (๐^2๐ฅ โ 1)/(๐^2๐ฅ + 1) Dividing numerator and denominator by ex, we obtain = (๐^2๐ฅ/๐^๐ฅ " " โ" " ๐/๐^๐ )/(๐^2๐ฅ/๐^๐ฅ " " + " " ๐/๐^๐ ) = (๐^๐ โ ๐^(โ๐))/(๐^๐ + ๐^(โ๐) ) Let ๐^๐ฅ + ๐^(โ๐ฅ)= ๐ก Differentiating both sides ๐ค.๐.๐ก.๐ฅ ๐^๐ฅ+(โ1) ๐^(โ๐ฅ)= ๐๐ก/๐๐ฅ ๐^๐ฅโ๐^(โ๐ฅ)= ๐๐ก/๐๐ฅ ๐๐ฅ=๐๐ก/(๐^๐ฅ โ ๐^(โ๐ฅ) ) Now, Integrating the function โซ1โใ" " (๐^2๐ฅ โ 1)/(๐^2๐ฅ + 1) " " ใ. ๐๐ฅ = โซ1โใ" " (๐^๐ฅ โ ๐^(โ๐ฅ))/(๐^๐ฅ + ๐^(โ๐ฅ) ) " " ใ. ๐๐ฅ (Using (๐^2๐ฅ โ 1)/(๐^2๐ฅ + 1)=(๐^๐ฅ โ ๐^(โ๐ฅ))/(๐^๐ฅ + ๐^(โ๐ฅ) ) ) Putting ๐^๐ฅ + ๐^(โ๐ฅ)=๐ก & ๐๐ฅ=๐๐ก/(๐^๐ฅ โ ๐^(โ๐ฅ) ) =โซ1โใ" " (๐^๐ฅ โ ๐^(โ๐ฅ))/๐ก " " ใ. ๐๐ก/(๐^๐ฅ โ ๐^(โ๐ฅ) ) " " =โซ1โใ" " 1/๐ก " " ใ. ๐๐ก =logโก|๐ก|+๐ถ =logโกใ |๐^๐ฅ+๐^(โ๐ฅ) |ใ+๐ถ =๐๐๐โก(๐^๐ + ๐^(โ๐) )+๐ช (Using ๐ก=๐^๐ฅ + ๐^(โ๐ฅ)) (As ๐^๐ฅ+๐^(โ๐ฅ)>0 )
Ex 7.2
Ex 7.2, 2
Ex 7.2, 3 Important
Ex 7.2, 4
Ex 7.2, 5
Ex 7.2, 6
Ex 7.2, 7 Important
Ex 7.2, 8
Ex 7.2, 9
Ex 7.2, 10
Ex 7.2, 11 Important
Ex 7.2, 12
Ex 7.2, 13
Ex 7.2, 14 Important
Ex 7.2, 15
Ex 7.2, 16
Ex 7.2, 17
Ex 7.2, 18
Ex 7.2, 19 Important You are here
Ex 7.2, 20 Important
Ex 7.2, 21
Ex 7.2, 22
Ex 7.2, 23
Ex 7.2, 24
Ex 7.2, 25
Ex 7.2, 26 Important
Ex 7.2, 27
Ex 7.2, 28
Ex 7.2, 29
Ex 7.2, 30
Ex 7.2, 31
Ex 7.2, 32 Important
Ex 7.2, 33 Important
Ex 7.2, 34 Important
Ex 7.2, 35
Ex 7.2, 36 Important
Ex 7.2, 37 Important
Ex 7.2, 38 Important
Ex 7.2, 39 Important
About the Author