If f(a - x) = f(x), then ∫[0 to a] x f(x) dx is equal to:
If f(a - x) = f(x), then ∫[0 to a] x f(x) dx is equal to:
- A. a/2 ∫[0 to a] f(x) dx
- B. a ∫[0 to a] f(x) dx
- C. 0
- D. -a/2 ∫[0 to a] f(x) dx
Answer: A) a/2 ∫[0 to a] f(x) dx
Explanation: Let I = ∫[0 to a] x f(x) dx. Using property, I = ∫[0 to a] (a - x) f(a - x) dx = ∫[0 to a] (a - x) f(x) dx = a ∫ f(x) dx - I. Thus 2I = a ∫ f(x) dx, giving I = a/2 ∫[0 to a] f(x) dx.
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