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COMEDK2015MathematicsDefinite Integration

If ₀^ x f( x) d x=A ₀^ / 2 f( x) d x , then A is equal to

Options

  1. A0
  2. B2
  3. C/4

Correct answer

3

Step-by-step solution

We have, array ll ₀^ x f( x) & d x=A ₀^ x / 2 f( x) d x Let I & = ₀^ x f( x) d x ...(i) I & = ₀^ ( -x) f( ( -x)) d x I & = ₀^ ( -x) f( x) d x ...(ii) array Adding Eqs. (i) and (ii), we get aligned &2 I= ₀^ f( x) d x I= 2 ₀^ f( x) d x & I= 2 2 ₀^ / 2 f( x) d x & I= ₀^ / 2 f( x) d x aligned On comparing, we get A=

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