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AP EAMCET202022 Sep 2020Morning ShiftMathematicsDefinite IntegrationActual

₀^ / 2 1 1+ ²⁰²⁰(x) d x=

Options

  1. A2
  2. B4
  3. C0

Correct answer

C. 0

Step-by-step solution

I= ₀^ / 2 d x 1+ ²⁰²⁰ x = ₀^ / 2 ²⁰²⁰ x ²⁰²⁰ x+ ²⁰²⁰ x d x On applying property ₀^a f(x) d x= ₀^a f(a-x) d x , we get I= ₀^ / 2 ²⁰²⁰ x ²⁰²⁰ x+ ²⁰²⁰ x d x On adding Eqs. (i) and (ii), we get 2 I= ₀^ / 2 d x= 2 I= 4 Hence, option (3) is correct.

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