Question 8 (OR 1 st question)

Find: ∫ e x (x - 3) / (x - 1) 3  dx

Slide18.JPG

Slide19.JPG

  1. Class 12
  2. Sample Papers, Previous Year Papers and Other Questions
Ask Download

Transcript

Question 8 (OR 1st question) Find: โˆซ1โ–’(๐‘’^๐‘ฅ (๐‘ฅ โˆ’ 3))/(๐‘ฅ โˆ’ 1)^3 dx โˆซ1โ–’(๐‘’^๐‘ฅ (๐‘ฅ โˆ’ 3))/(๐‘ฅ โˆ’ 1)^3 dx = โˆซ1โ–’(๐‘’^๐‘ฅ (๐‘ฅ โˆ’ 1 โˆ’ 2))/(๐‘ฅ โˆ’ 1)^3 dx = โˆซ1โ–’(๐‘’^๐‘ฅ [(๐‘ฅ โˆ’ 1)โˆ’ 2])/(๐‘ฅ โˆ’ 1)^3 dx = โˆซ1โ–’ใ€–๐‘’^๐‘ฅ [((๐‘ฅ โˆ’ 1) โˆ’ 2)/(๐‘ฅ โˆ’ 1)^3 ] ใ€— dx = โˆซ1โ–’ใ€–๐‘’^๐‘ฅ [((๐‘ฅ โˆ’ 1))/(๐‘ฅ โˆ’ 1)^3 +((โˆ’2)/(๐‘ฅ โˆ’ 1)^3 )] ใ€— dx = โˆซ1โ–’ใ€–๐‘’^๐‘ฅ [1/(๐‘ฅ โˆ’ 1)^2 +((โˆ’2)/(๐‘ฅ โˆ’ 1)^3 )] ใ€— dx It is of form โˆซ1โ–’ใ€–๐‘’^๐‘ฅ (๐‘“(๐‘ฅ)+๐‘“^โ€ฒ (๐‘ฅ)) ใ€— ๐‘‘๐‘ฅ=๐‘’^๐‘ฅ ๐‘“(๐‘ฅ)+๐ถ Putting, ๐‘“(๐‘ฅ)=1/(๐‘ฅ โˆ’ 1)^2 " " โˆด ๐‘“^โ€ฒ (๐‘ฅ)= (โˆ’2)/(๐‘ฅ โˆ’ 1)^3 โˆซ1โ–’ใ€–๐‘’^๐‘ฅ [1/(๐‘ฅ โˆ’ 1)^2 +((โˆ’2)/(๐‘ฅ โˆ’ 1)^3 )] ใ€— dx =๐’†^๐’™/(๐’™ โˆ’ ๐Ÿ)^๐Ÿ +๐‘ช

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.