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MHT CET202310 May 2023Evening ShiftMathematicsDefinite IntegrationActual

Let f: R R and g: R R be continuous functions. Then the value of the integral _ - 2 ^ 2 [ f (x)+ f (-x)][ g (x)- g (-x)] d x is

Options

  1. A1
  2. B-1
  3. C0

Correct answer

3

Step-by-step solution

Let h (x)=[ f (x)+ f (-x)][ g (x)- g (-x)] aligned h (-x) & =[ f (-x)+ f (x)][ g (-x)- g (x)] & =-[ f (x)+ f (-x)][ g (x)- g (-x)] & =- h (x) aligned h (x) is an odd function. _ - 2 ^ 2 ~h (x)=0

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