- #1

ehrenfest

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**[SOLVED] Rudin's change of variables theorem**

## Homework Statement

Rudin's Principles of Mathematical Analysis Theorem 6.19 (for the Riemann integral case) says

Suppose \phi is a strictly increasing continuous differentiable function that maps an interval [A,B] ont [a,b]. Suppose f is Riemann integrable on [a,b]. THen

[tex]\int_a^b f(x) dx = \int_A^B f(\phi(y)) \phi'(y) dy [/tex]

I am kind of confused about why Rudin threw in the stipulation that \phi should be strictly increasing. I thought it only need to be continuously differentiable...