8. If f is continuous on [a, b] and there exist numbers a =1= f3 such that
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8. If f is continuous on [a, b] and there exist numbers a =1= f3 such that a Ic f(x) dx + f31b f(x) dx = 0 holds for all c E
(a, b), prove that f(x) = 0 for all x E [a, b].
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