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

Last updated at Dec. 23, 2019 by Teachoo

Transcript

Misc 29 Evaluate the definite integral โซ_0^1โใ๐๐ฅ/(โ(1 + ๐ฅ) โ โ๐ฅ) ใ โซ_0^1โใ๐๐ฅ/(โ(1 + ๐ฅ) โ โ๐ฅ) ใ Rationalizing i.e., multiplying and dividing by (โ(1 + ๐ฅ)+โ๐ฅ) = โซ_0^1โใ๐๐ฅ/(โ(1 + ๐ฅ) โ โ๐ฅ) ใร(โ(1 + ๐ฅ) + โ๐ฅ)/(โ(1 + ๐ฅ) + โ๐ฅ) . ๐๐ฅ = โซ_0^1โ(โ(1 + ๐ฅ) + โ๐ฅ)/((โ(1 + ๐ฅ) )^2 โ (โ๐ฅ )^2 ) . ๐๐ฅ = โซ_0^1โ(โ(1 + ๐ฅ) + โ๐ฅ)/(1 + ๐ฅ โ ๐ฅ) . ๐๐ฅ = โซ_0^1โ(โ(1 + ๐ฅ) + โ๐ฅ)/1 . ๐๐ฅ = โซ_0^1โโ(1+๐ฅ) . ๐๐ฅ+โซ_0^1โโ๐ฅ . ๐๐ฅ" " = โซ_0^1โ(1+๐ฅ)^(1/2) ๐๐ฅ+โซ_0^1โ(๐ฅ)^(1/2) ๐๐ฅ" " = [(1 + ๐ฅ)^(1/2 + 1)/(1/2 + 1)]_0^1 + [ใ๐ฅ ใ^(1/2 + 1)/(1/2 + 1)]_0^1 = [(1 + ๐ฅ)^(3/2)/(3/2)]_0^1 + [ใ๐ฅ ใ^(3/2)/(3/2)]_0^1 = ใ2/3 [(1+๐ฅ)^(3/2) ]ใ_0^1 + 2/3 [ใ๐ฅ ใ^(3/2) ]_0^1 = 2/3 [(1+1)^(3/2)โ(1+0)^(3/2) ] + 2/3 [(1)^(3/2)โ(0)^(3/2) ] = 2/3 [(2)^(3/2)โ(1)^(3/2) ] + 2/3 [1โ0] = 2/3 . (2)^(3/2)โ2/3 [1]+2/3 [1] = 2/3 (2)^(3/2) = 2/3 [(2)^(1/2) ]^3 = 2/3 (โ2 )^3 = 2/3 . 2 โ2 = (๐ โ๐)/๐

Miscellaneous

Misc 1
Important

Misc 2 Important

Misc 3 Important

Misc 4

Misc 5 Important

Misc 6

Misc 7 Important

Misc 8 Important

Misc 9

Misc 10 Important

Misc 11

Misc 12

Misc 13

Misc 14 Important

Misc 15

Misc 16

Misc 17

Misc 18 Important

Misc 19 Important

Misc 20 Important

Misc 21

Misc 22

Misc 23

Misc 24 Important

Misc 25 Important

Misc 26 Important

Misc 27 Important

Misc 28 Important

Misc 29 You are here

Misc 30 Important

Misc 31 Important

Misc 32 Important

Misc 33 Important

Misc 34

Misc 35

Misc 36

Misc 37

Misc 38 Important

Misc 39

Misc 40 Important

Misc 41 Important

Misc 42

Misc 43

Misc 44 Important

Integration Formula Sheet - Chapter 7 Class 12 Formulas Important

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.