Given a transformation of coordinates
$$ \bar{x} = \frac{x}{x_0} $$
how do I change the coordinates on the integral:
$$ I_1 = \int_a^b {f(x)}dx\\ $$
And how do I change it if my function is defined as:
$$ I_2(x) = \int_0^x {f(\tau)d\tau} $$
Integral 1 seems to be straightforward: $$ x=x_0\ \bar{x}\rightarrow dx=x_0\ d\bar{x} $$
$$ I_1 = x_0\ \int_c^d {f(x_0\ \bar{x})}d\bar{x} \\ $$
Does integral 2 just change the limits?
$$ I_2(\bar{x}) = \int_0^{x_0\ \bar{x}} {f(\tau)d\tau} $$