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AP EAMCET202123 Aug 2021Evening ShiftMathematicsDefinite IntegrationActual

_ 2 e ^ 1 e 1 [x( x)^ 1 3 ] d x is equal to

Options

  1. A3 2 1+( (2)-1)^ 2 3
  2. B1
  3. C3 2 1+( (2)+1)^ 3 2
  4. D3 2 1-( (2)-1)^ 2 3

Correct answer

D. 3 2 1-( (2)-1)^ 2 3

Step-by-step solution

Let I- _ 2 / e ^ 1 / e 1 x( x)^ 1 / 3 d x Let x=t Upper limit t= 1 / e=-1 1 x d x=d t lower limit t= 2 / e aligned & = 2- e & = 2-1 aligned I= _ 2-1 ⁻¹ d t t^ 1 / 3 aligned & = . t^ -1 / 3+1 -1 / 3+1 |_ 2-1 ⁻¹ & = 3 2 ((-1)^ 2 / 3 -( 2-1)^ 2 / 3 ) aligned I= 3 2 [1-( 2-1)^ 2 / 3 ]

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