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AP EAMCET202418 May 2024Morning ShiftMathematicsDefinite IntegrationActual

_ 4 ^ 5 e^ 2 x +e^x e^ 2 x -5 e^x+6 d x=

Options

  1. A( 64 9 )
  2. B( 256 81 )
  3. C( 32 3 )
  4. D( 128 27 )

Correct answer

D. ( 128 27 )

Step-by-step solution

Let I = _ 4 ^ 5 e^ 2 x +e^x e^ 2 x -5 e^x+6 d x= _ 4 ^ 5 e^x (e^x+1 ) (e^x-3 ) (e^x-2 ) d x aligned & Let e ^x=t e ^x d x=d t & I = ₄^5 t+1 (t-3)(t-2) d t aligned = ₄^5 ( 4 t-3 - 3 t-2 ) d t=[4 (t-3)-3 (t-2)]₄^5 aligned & =4 2-3 3-4 1+3 2 & =7 2-3 3= ( 128 27 ) aligned

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