I was playing with an equation using what I think it is called "infinitesimal calculus" and I arrived at this equation form:
$$ f(t) = g(x)p_t(x)dx $$
where $f(t)$ and $p_t(x)$ are both probability density functions.
I don't know how to deal with it or how to get rid of it rather.
I thought
$$ p_t(x)dx = P_t(x + dx) - P_t(x) $$
where $P_t(x)$ is the cumulative function. This gives me the wrong answer.
Any advice?
Edit
So based on some really good comments - I checked my math and I realized that
$$f(t) \neq h(t)dt$$