$$\int x\ dx=\int \underbrace{(1 + 1 + \cdots + 1)}_{x\text{ times}}\ dx=x^2$$ Is the algebra Ok? The professor said that the function looses continuity; could anybody explain that?
Flaw in calculation of $\int x \, dx=x^2$
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integration
continuity
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8What does "$x$ times" mean when $x=\frac{1}{2}$? – 2012-09-27
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0Someone posted the question of where the error is in this argument a few weeks ago. I posted a reply. Maybe this isn't quite a duplicate question, but perhaps the same reply would work here. – 2012-09-27
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2Even without losing continuity this remains wrong: Compare $$\sum_{k=1}^n k =\sum_{k=1}^n \underbrace{1+1+\ldots +1}_{n} = n^2??$$ – 2012-09-27
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0Is the problem written correctly? The integral result is wrong from the start. Was he trying to show that if you sum some set of rectangles you get the same results? Regardless, the title is wrong from the start. – 2012-09-27