Chapter 7 Class 12 Integrals
Concept wise

Example 36 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by

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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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