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NDA2021MathematicsDefinite IntegrationActual

If ₀^a[f(x)+f(-x)] d x= _ -a ^a g(x) d x then what is g(x) equal to?

Options

  1. Af(x)
  2. Bf(-x)+f(x)
  3. C-f(x)
  4. DNone of the above

Correct answer

A. f(x)

Step-by-step solution

₀^a[f(x)+f(-x)] d x= _ -a ^a g(x) d x aligned & = _ -a ^0 g(x) d x+ ₀^a g(x) d x & = ₀^a g(-x) d x+ ₀^a g(x) d x aligned = ₀^a[g(x)+g(-x)] d x f(x)=g(x)

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