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NDA2021MathematicsDefinite IntegrationActual

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

Options

  1. Aa
  2. B2 a
  3. C0
  4. Da 2

Correct answer

D. a 2

Step-by-step solution

aligned I & = ₀^a f(a-x) f(x)+f(a-x) d x & = ₀^a f(a+0-a+x) f(a+0-x)+f(a+0-a+x) d x aligned aligned & = ₀^a f(x) f(a-x)+f(x) d x & 2 I= ₀^a f(a-x)+f(x) f(a-x)+f(x) d x=[x]₀^a aligned I= a 2

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