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The statement “Every integrable function is monotonic” is false. To see why, first clarify the terms used: in elementary calculus “integrable” usually means Riemann integrable on a closed, bounded interval $[a,b]$. Even under that interpretation the claim fails — there are plenty of Riemann integrable functions that are not monotonic. ______ __________ ____ _________ _____ _____ ______ __________ _____.
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