5.2.2. a) Suppose that a < b and n € N is even. If f is continuous on [a, b] and f f(x)x"dx = 0, prove that f(x) = 0 for at least one x € [a, b]. b) Show that part a) might not be true if n is odd.

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5.2.2. a) Suppose that a < b and n € N is even. If f is continuous on [a, b] and
f f(x)x"dx = 0, prove that f(x) = 0 for at least one x € [a, b].
b) Show that part a) might not be true if n is odd.
Transcribed Image Text:5.2.2. a) Suppose that a < b and n € N is even. If f is continuous on [a, b] and f f(x)x"dx = 0, prove that f(x) = 0 for at least one x € [a, b]. b) Show that part a) might not be true if n is odd.
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