If I have an improper integral $\displaystyle \int_{a}^{b}f(x)dx$,
and $b$ is the improper extrem, if $f(x)\sim g(x)$ for $x->b^-$, the integrals $\displaystyle \int_{a}^{b}f(x)dx$ and $\displaystyle \int_{a}^{b}g(x)dx$have the same behaviour.
But is it true also if the improper extreme is $a$ and I have that $f(x)\sim g(x)$ for $x->a^+$?
My textbook doesn't say anything about it...