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can you explain that last two steps? how that $$na(n)r^{n-1}$$ disappeared in next integral?I noticed the transformation of variables but still not able to figure out properly.

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Note that in Evans $n\alpha(n)$ is the surface area of the unit sphere in $\mathbb{R}^n$, so that $$ \int_0^{\varepsilon}{\eta}\Bigl(\frac{r}{\varepsilon}\Bigr)n\alpha(n)r^{n-1}dr= \int_0^{\varepsilon}\biggl(\int_{\partial B(0,r)}\eta\Bigl(\frac{r}{\varepsilon}\Bigr)\,dS\biggr)\,dr= \int_{B(0,\varepsilon)}\eta\Bigl(\frac{r}{\varepsilon}\Bigr)\,dy. $$

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