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!
Integral where limit of bounds both goes to infinity
0
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improper-integrals
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1Does $\int_a^{\infty}F(x)\mathrm{d}x$ converge for some value $a$? – 2017-01-18
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2What happens if $F(x)=1$? – 2017-01-18
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0how 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) – 2017-01-18
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0If you're trying to reason along the lines that $\int_a^a f(x)\; dx=0$, then this isn't good enough. – 2017-01-18