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प्रश्न

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

विकल्प

  • `15/16`

  • `3/16`

  • `-3/16`

  • `-16/3`

MCQ
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उत्तर

`-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
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 20: Definite Integrals - MCQ [पृष्ठ ११९]

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 20 Definite Integrals
MCQ | Q 28 | पृष्ठ ११९

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