# A question regarding to the proof of multivariable changing of variables formula.

In the proof of Theorem 5.5 on the below image, where does the n/6A term come from?

Expanding on my comment, this is what I think it means. It would be useful to have Theorem 3.4 to be able to be completely sure, but I think the idea is that for any $\epsilon \gt 0$, $\exists \delta$ such that given any partition $P$ with $\text{mesh}\ P \lt \delta$, the difference between the Riemann sum associated with $P$ and the integral is less than $\epsilon$. Here, we take $\epsilon$ to be $\frac{\eta}{12A}$, and we know that $\exists \delta_2$ satisfying the above condition. Why $\frac{\eta}{12A}$? Without seeing the next page of the book, I can only guess that eventually that $12A$ will go away and we'll be left with $\eta$ alone. If you had started with $\eta$ instead of $\frac{\eta}{12A}$, we would end up with an extra $12A$ around.