Thread: riemann integrable
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Old December 3rd, 2008, 04:24 PM
Plato Plato is offline
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Here is a hint.
If \left( {\exists c \in [a,b]} \right)\left[ {f(c) > 0} \right] then \left( {\exists [d,e] \subseteq [a,b]} \right)\left( {\forall z \in [d,e]} \right)\left[ {f(z) > \frac{{f(c)}}{2}} \right].
Ask yourself what is the minimum value of \int_d^e {f(x)dx}.

Now drop continuity: f(x) = \left\{ {\begin{array}{rl} {1/n} & {x = a + 1/n} \\ 0 & {else} \\ \end{array} } \right..
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