Chapter 7 Class 12 Integrals
Concept wise

Ex 7.2, 12 - Integrate (x3 - 1)1/3 .x5 - Chapter 7 CBSE - Integration by substitution - x^n

Ex 7.2, 12 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.2, 12 - Chapter 7 Class 12 Integrals - Part 3
Ex 7.2, 12 - Chapter 7 Class 12 Integrals - Part 4

Go Ad-free

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‘Ÿ.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 โˆซ1โ–’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 ) = โˆซ1โ–’ใ€–" " (๐‘ก โ€“ 1)^(1/3) . ๐‘ฅ5ใ€— . ๐‘‘๐‘ก/(3๐‘ฅ^2 ) = โˆซ1โ–’ใ€–" " (๐‘ก โ€“ 1)^(1/3) . ๐‘ฅ^2. ๐‘ฅ^3 ใ€—. ๐‘‘๐‘ก/(3๐‘ฅ^2 ) = โˆซ1โ–’ใ€–" " (๐‘ก โ€“ 1)^(1/3) ใ€— . ๐‘ฅ^3/3 . ๐‘‘๐‘ก = โˆซ1โ–’ใ€–" " (๐‘ก โ€“ 1)^(1/3) ใ€— . ๐‘ก/3 . ๐‘‘๐‘ก = 1/3 โˆซ1โ–’ใ€–" " (๐‘ก โ€“ 1)^(1/3) ใ€— . ๐‘ก . ๐‘‘๐‘ก = 1/3 โˆซ1โ–’ใ€–" " (๐‘ก โ€“ 1)^(1/3) ใ€— . (๐‘กโˆ’1+1) ๐‘‘๐‘ก = 1/3 โˆซ1โ–’ใ€–" " (๐‘ก โ€“ 1)^(1/3) ใ€— . ((๐‘กโˆ’1)+1) ๐‘‘๐‘ก = 1/3 โˆซ1โ–’((๐‘ก โ€“ 1)^(1/3) (๐‘กโˆ’1)+(๐‘กโˆ’1)^(1/3) ) ๐‘‘๐‘ก = 1/3 โˆซ1โ–’((๐‘ก โ€“ 1)^(1/3 +1)+(๐‘กโˆ’1)^(1/3) ) ๐‘‘๐‘ก = 1/3 โˆซ1โ–’((๐‘ก โ€“ 1)^(4/3 )+(๐‘กโˆ’1)^(1/3) ) ๐‘‘๐‘ก = 1/3 โˆซ1โ–’ใ€– (๐‘ก โ€“ 1)^(4/3 ). ๐‘‘๐‘กใ€— + 1/3 โˆซ1โ–’ใ€– (๐‘ก โ€“ 1)^(1/3 ). ๐‘‘๐‘กใ€— = 1/3 โˆซ1โ–’ใ€– (๐‘ก โ€“1)^(4/3 ). ๐‘‘๐‘กใ€— + 1/3 โˆซ1โ–’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 โˆ’ 1)^(7/3)/(7/3) + 1/3 (๐‘ก โˆ’ 1)^(4/3)/(4/3) + ๐ถ = 1/7 (๐‘กโˆ’1)^(7/3) +1/4 (๐‘กโˆ’1)^(4/3) +๐ถ = ๐Ÿ/๐Ÿ• (๐’™^๐Ÿ‘ โ€“๐Ÿ)^(๐Ÿ•/๐Ÿ‘) + ๐Ÿ/๐Ÿ’ (๐’™^๐Ÿ‘โ€“๐Ÿ)^(๐Ÿ’/๐Ÿ‘) + ๐‘ช

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.