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1 ∫ 0 X ( 1 − X ) 5 4 D X = - Mathematics

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Question

\[\int\limits_0^1 \frac{x}{\left( 1 - x \right)^\frac{5}{4}} dx =\]

Options

  • `15/16`

  • `3/16`

  • `-3/16`

  • `-16/3`

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Solution

`-16/3`

 

`I=int_0^1x/(1-x)^(5/4)dx`

Put, 1 - x = t ⇒ x = 1 - t

⇒ dx = -dt

x 0 1
t 1 0

`I=int_1^0((1-t)(-dt))/t^(5/4)`

`I=int_0^1(1-t)/t^(5/4)dt`

`I=int_0^1(t^(-5/4)-t^(-1/4))dt`

`I=[t^(-1/4)/(-1/4)-t^(3/4)/(3/4)]_0^1`

`I=-4-4/3`

`I=-16/3`

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Definite Integrals
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Chapter 20: Definite Integrals - MCQ [Page 119]

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RD Sharma Mathematics [English] Class 12
Chapter 20 Definite Integrals
MCQ | Q 28 | Page 119

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