if $\int_{0}^{\infty}g(x)dx=-\infty$ and $g(x)$ is a continues function.
then by which theorem one can conclude that $g(\infty)<=0$?
2026-04-06 19:09:17.1775502557
if $\int_{0}^{\infty}g(x)dx=-\infty$ then $g(\infty)<=0$?
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No, consider for example $$ g(x)=\sin x-\frac{1}{4}. $$