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AP EAMCET202022 Sep 2020Morning ShiftMathematicsDefinite IntegrationActual

₀^1(1+x) (1+x) d x=

Options

  1. A-3 4 + 2
  2. B3 4 +2 2
  3. C2 2
  4. D-3 4 +2 2

Correct answer

D. -3 4 +2 2

Step-by-step solution

aligned I & = ₀^1(1+x) (1+x) d x & = [( (1+x)) (x+ x^2 2 ) ]₀^1- ₀^1 (x+ x^2 2 ) 1+x d x & = 3 2 _e 2- 1 2 ₀^1 [(x+1)- 1 1+x ] d x & = 3 2 _e 2- 1 2 [ x^2 2 +x- _e(1+x) ]₀^1 aligned aligned & = 3 2 _e 2- 1 2 [ 1 2 +1- 2 ] & =2 ( _e 2 )- 3 4 =- 3 4 +2 _e 2 aligned

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