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JEE Main2006MathematicsDefinite IntegrationActual

₀^ x f( x) d x is equal to

Options

  1. A₀^ f( x) d x
  2. B₀^ f( x) d x
  3. C2 ₀^ / 2 f( x) d x
  4. D₀^ / 2 f( x) d x

Correct answer

D. ₀^ / 2 f( x) d x

Step-by-step solution

I= ₀^ x f( x) d x= ₀^ ( -x) f( x) d x= ₀^ f( x) d x-12 I= ₀^ f( x) d xI= 2 ₀^ f( x) d x= ₀^ / 2 f( x) d x= ₀^ / 2 f( x) d x

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