Prove or disprove by counterexample the statement: $(\forall x \in [a; b]$ $f(x) < g(x))\Rightarrow $ $$\Rightarrow (\int_{a}^bf(x)dx < \int_{a}^bg(x)dx)$$ Of course, f and g are integrable on [a; b].
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Have you tried anything yourself? – eyeballfrog May 04 '20 at 21:36
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Sure, I've tried to disprove it by counterexample but, unforunately, I haven't find the correct one... – Aren Bit May 04 '20 at 21:39
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1Have you tried proving it true? Also, you should edit any work you've done into the question. – eyeballfrog May 04 '20 at 21:44
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1Hint: Ask yourself can you construct a function which is strictly positive but may have a zero area. – Anurag A May 04 '20 at 21:44
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Thank you, Anurag A! – Aren Bit May 04 '20 at 21:59