Within an exercise, I was wondering about this step of solving an equation:
\begin{align} \int_0^s \frac{\dot{z}(t)}{f(z(t))} \text{d}t = s \\ \Leftrightarrow \int_{z(0)}^{z(s)} \frac{1}{f(z(t))} \text{d}t = s \end{align}
It seems easy, but Im confused about why this holds; Im thinking something to do with coordinate transformation or Jacobian determinate, but I better ask y'all. Any idea?
Thanks