Question: Suppose that a > 0 and that f R[-a, a]. (a) If f is even (that is, if f (-x) = f(x) for all

Suppose that a > 0 and that f ∈ R[-a, a].
(a) If f is even (that is, if f (-x) = f(x) for all x ∈ [0, a], show that ∫a-a f = 2 ∫a0 f.
(b) If f is odd (that is, if f (-x) = -f(x) for all x ∈ [0, a], show that ∫a-a f = 0.

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