Change of Variables Formula
Saturday, 9 June 2018
6:04 PM
Created with Microsoft OneNote 2016.
![Machine generated alternative text:
In general, the reversal of the chain rule via integration gives rise to the change of variables
formula
g(b)
f (u) du,
g(a)
The substitutions
du — g'(x) da;,
(8.19)
are only to be understood within this context. Precise conditions under which formula (8.19) holds
is given by the following theorem.
CHAPTER 8. INTEGRATION
Theorem 8.8.3 (Change of variables formula). Suppose that g is a differentiable function such
that g' is continuous on [a, b]. If f is continuous on any interval I containing g(a) and g(b) then
the change of variables formula (8.19) holds.](Change%20of%20Variables%20Formula_files/image001.png)