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AP EAMCET202017 Sep 2020Morning ShiftMathematicsDefinite IntegrationActual

( ₁^ e^2 d x x(1+ x)^2 = )

Options

  1. A( 2 3 )
  2. B( 1 3 )
  3. C( 3 2 )
  4. D( 2 )

Correct answer

A. ( 2 3 )

Step-by-step solution

(I= ₁^ e^2 d x x(I+ x)^2 ) Let ( 1+ x=t ) ( 1 x d x=d t ) ( I= ₁^3 d t t^2 = [ t⁻¹ -1 ]₁^3= ( 3⁻¹ -1 + 1⁻¹ 1 ) ) (I=- 1 3 +1= 2 3 )

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