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Manipal MET2017MathematicsDefinite Integration

₀^ 2 a f(x) f(x)+f(2 a-x) d x is equal to

Options

  1. Aa
  2. B-a
  3. C1
  4. D0

Correct answer

A. a

Step-by-step solution

Let I= ₀^ 2 a f(x) f(x)+f(2 a-x) d x...(i)I= ₀^ 2 a f(2 a-x) f(2 a-x)+f(x) d x...(ii) On adding Eqs. (i) and (ii), we get aligned 2 I & = ₀^ 2 a f(2 a-x)+f(x) f(2 a-x)+f(x) d x= ₀^ 2 a d x=2 a I & =a aligned

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