$\int xdx$ as upper bound goes to infinity and lower bound goes to negative infinity.
$\int xdx$ as the bounds go to finite b and -b exists and is always equal to 0. Does that mean that this integral exists as an improper integral?
Thanks!
2026-04-03 02:16:39.1775182599
Does this integral exist as improper Riemann integral?
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No. You have shown that if it exists then it is equal to $0$. But in order for the integral to exist, it must be well-defined however you take the limit; and if you take the upper limit to infinity twice as fast as you take the lower limit, you'll get the answer $\infty$, which is definitely not $0$.