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AP EAMCET2006MathematicsDefinite Integration

₀^ / 2 d x 1+ ^3 x is equal to :

Options

  1. A2
  2. B4
  3. C3 2

Correct answer

C. 3 2

Step-by-step solution

I= ₀^ / 2 d x 1+ ^3 x I= ₀^ / 2 ^3 x ^3 x+ ^3 x d x ...(i) I= ₀^ / 2 ^3 ( 2 -x ) ^3 ( 2 -x )+ ^3 ( 2 -x ) d xI= ₀^ / 2 ^3 x ^3 x+ ^3 x d x ...(ii) On adding Eqs. (i) and (ii), we get 2 I= ₀^ / 2 ^3 x+ ^3 x ^3 x+ ^3 x d x= ₀^ / 2 1 d x= 2 I= 4

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