Let $T>0,$ $w >\!\!> T$ and let $f:\mathbb{R} \to \mathbb{R}$ be $T-$ periodic function.
I'd like to know whether there is a quadrature formula with number of points independent of $w$ for
$$I= \int_a^b f(w x)dx$$ which approximates $I$ at the order $\mathcal{O}(w^{-m})$ for some positive integer $m.$
Thank you in advanced