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

Last updated at Dec. 20, 2019 by Teachoo
Transcript
Ex 7.11,7 By using the properties of definite integrals, evaluate the integrals : โซ_0^1โใ ๐ฅ(1โ๐ฅ)^๐ ใ ๐๐ฅ Let I=โซ_0^1โใ๐ฅ(1โ๐ฅ)^๐ ๐๐ฅใ โด I=โซ_0^1โใ(1โ๐ฅ) [1โ(1โ๐ฅ)]^๐ ๐๐ฅใ I=โซ_0^1โใ(1โ๐ฅ) [1โ1+๐ฅ]^๐ ๐๐ฅใ I=โซ_0^1โใ(1โ๐ฅ) [๐ฅ]^๐ ๐๐ฅใ I= โซ_0^1โใ(1โ๐ฅ) ใ ๐ฅใ^๐ ๐๐ฅใ Using P4 : โซ_0^๐โใ๐(๐ฅ)๐๐ฅ=ใ โซ_0^๐โ๐(๐โ๐ฅ)๐๐ฅ I= โซ_0^1โใ(ใ ๐ฅใ^๐โ ๐ฅ^(๐ + 1) ) ๐๐ฅใ I= โซ_0^1โใใ ๐ฅใ^๐ ๐๐ฅใโโซ_0^1โใใ ๐ฅใ^(๐ + 1) ๐๐ฅใ I=[๐ฅ^(๐ + 1)/(๐ + 1)]_0^1โ[๐ฅ^(๐ + 2)/(๐ + 2)]_0^1 I=[(1)^(๐ + 1)/(๐ + 1)โ(0)^(๐ + 1)/(๐ + 1)]โ[(1)^(๐ + 2)/(๐ + 2)โ(0)^(๐ + 2)/(๐ + 2)] I= 1/(๐ + 1)โ1/(๐ + 2) I=(๐ + 2 โ (๐ + 1))/(๐ + 1)(๐ + 2) ๐=๐/(๐ + ๐)(๐ + ๐)
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