Check sibling questions

Example 38 - Evaluate integral (x4 - x)1/4 / x5 dx - Examples

Example 38 - Chapter 7 Class 12 Integrals - Part 2


Transcript

Example 38 Evaluate ∫1β–’(π‘₯^4 βˆ’π‘₯)^(1/4)/π‘₯^5 𝑑π‘₯ ∫1β–’(π‘₯^4 βˆ’ π‘₯)^(1/4)/π‘₯^5 𝑑π‘₯ Taking π‘₯^4 common from numerator =∫1β–’γ€–(π‘₯^4 )^(1/4) (1 βˆ’ π‘₯/π‘₯^4 )γ€—^(1/4)/π‘₯^5 𝑑π‘₯ = ∫1β–’(π‘₯ (1 βˆ’ 1/π‘₯^3 )^(1/4))/π‘₯^5 𝑑π‘₯ = ∫1β–’(1 βˆ’ 1/π‘₯^3 )^(1/4)/π‘₯^4 𝑑π‘₯ Let t = 1 βˆ’ 1/π‘₯^3 𝑑𝑑/𝑑π‘₯=3/π‘₯^4 Substituting values, =∫1▒〖𝑑 γ€—^(1/4)/3 𝑑𝑑 = 1/3 (𝑑^( 1/(4 ) + 1)/(1/4 +1))+ C = 1/3 ((𝑑^( 5/4) )/(5/4))+ C = 4/15 〖𝑑 γ€—^(5/4)+ C = πŸ’/πŸπŸ“ (πŸβˆ’πŸ/𝒙^πŸ‘ )^( πŸ“/πŸ’)+ C

Davneet Singh's photo - Teacher, Engineer, Marketer

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.