does the following expression goes to zero?
$$\lim_{x \rightarrow + \infty} \int_{x}^{+\infty} F(x)dx$$
My thinking process is that since the bounds of the integral are converging to the same "value", it should collapse. Is this correct? Thank you!
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2Does $\int_a^{\infty}F(x)\mathrm{d}x$ converge for some value $a$? – user404127 Jan 18 '17 at 15:22
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2What happens if $F(x)=1$? – Brian Borchers Jan 18 '17 at 15:22
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how about a function F(x) = 1 / (x - [x]) where [x] is the floor function (largest integer less than x) then however large x is, there is always an infinity of infinite areas ahead of it - but I don't really know what the answer is supposed to be though! I sort of think it could be unbounded, for some F(x) – Cato Jan 18 '17 at 15:24
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If you're trying to reason along the lines that $\int_a^a f(x); dx=0$, then this isn't good enough. – MPW Jan 18 '17 at 15:27