Example 36 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 36 Evaluate ∫1▒(𝑥^4 −𝑥)^(1/4)/𝑥^5 𝑑𝑥 ∫1▒(𝑥^4 − 𝑥)^(1/4)/𝑥^5 𝑑𝑥 Taking 𝑥^4 common from numerator =∫1▒〖(𝑥^4 )^(1/4) (1 − 𝑥/𝑥^4 )〗^(1/4)/𝑥^5 𝑑𝑥 = ∫1▒(𝑥 (1 − 1/𝑥^3 )^(1/4))/𝑥^5 𝑑𝑥 = ∫1▒(1 − 1/𝑥^3 )^(1/4)/𝑥^4 𝑑𝑥 Let t = 1 − 1/𝑥^3 𝑑𝑡/𝑑𝑥=3/𝑥^4 Substituting values, =∫1▒〖𝑡 〗^(1/4)/3 𝑑𝑡 = 1/3 (𝑡^( 1/(4 ) + 1)/(1/4 +1))+ C = 1/3 ((𝑡^( 5/4) )/(5/4))+ C = 4/15 〖𝑡 〗^(5/4)+ C = 𝟒/𝟏𝟓 (𝟏−𝟏/𝒙^𝟑 )^( 𝟓/𝟒)+ C
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About the Author
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 and Computer Science at Teachoo