Ex 7.2

Chapter 7 Class 12 Integrals
Serial order wise

### Transcript

Ex 7.2, 12 Integrate the function: (๐ฅ3 โ 1)^(1/3) . ๐ฅ5 (๐ฅ3 โ 1)^(1/3) . ๐ฅ5 Step 1: Let ๐ฅ3= ๐ก Differentiating both sides ๐ค.๐.๐ก.๐ฅ 3๐ฅ^2= ๐๐ก/๐๐ฅ 3๐ฅ^2. d๐ฅ=๐๐ก ๐๐ฅ = ๐๐ก/(3๐ฅ^2 ) Step 2: Integrating the function โซ1โใ" " (๐ฅ3 โ 1)^(1/3) . ๐ฅ5" " ใ . ๐๐ฅ Putting the value of ๐ฅ^3 & ๐๐ฅ=๐๐ก/(3๐ฅ^2 ) = โซ1โใ" " (๐ก โ 1)^(1/3) . ๐ฅ5ใ . ๐๐ก/(3๐ฅ^2 ) = โซ1โใ" " (๐ก โ 1)^(1/3) . ๐ฅ^2. ๐ฅ^3 ใ. ๐๐ก/(3๐ฅ^2 ) = โซ1โใ" " (๐ก โ 1)^(1/3) ใ . ๐ฅ^3/3 . ๐๐ก = โซ1โใ" " (๐ก โ 1)^(1/3) ใ . ๐ก/3 . ๐๐ก = 1/3 โซ1โใ" " (๐ก โ 1)^(1/3) ใ . ๐ก . ๐๐ก = 1/3 โซ1โใ" " (๐ก โ 1)^(1/3) ใ . (๐กโ1+1) ๐๐ก = 1/3 โซ1โใ" " (๐ก โ 1)^(1/3) ใ . ((๐กโ1)+1) ๐๐ก = 1/3 โซ1โ((๐ก โ 1)^(1/3) (๐กโ1)+(๐กโ1)^(1/3) ) ๐๐ก = 1/3 โซ1โ((๐ก โ 1)^(1/3 +1)+(๐กโ1)^(1/3) ) ๐๐ก = 1/3 โซ1โ((๐ก โ 1)^(4/3 )+(๐กโ1)^(1/3) ) ๐๐ก = 1/3 โซ1โใ (๐ก โ 1)^(4/3 ). ๐๐กใ + 1/3 โซ1โใ (๐ก โ 1)^(1/3 ). ๐๐กใ = 1/3 โซ1โใ (๐ก โ1)^(4/3 ). ๐๐กใ + 1/3 โซ1โใ (๐ก โ1)^(1/3 ). ๐๐กใ = 1/3 (๐ก โ1)^(4/3 + 1)/(4/3 + 1) + 1/3 (๐ก โ1)^(1/3 + 1)/(1/3 + 1) + ๐ถ = 1/3 (๐ก โ 1)^(7/3)/(7/3) + 1/3 (๐ก โ 1)^(4/3)/(4/3) + ๐ถ = 1/7 (๐กโ1)^(7/3) +1/4 (๐กโ1)^(4/3) +๐ถ = ๐/๐ (๐^๐ โ๐)^(๐/๐) + ๐/๐ (๐^๐โ๐)^(๐/๐) + ๐ช