$\int_a^b\,f(x)\,dx$ definite integral of $f(x)$ Paragraph
$\int\,f(x)\,dx$ indefinite integral of $f(x)$ Definition 2.2
$\rho$ this symbol could be used for lots of things, but we are just trying to make a super-long description to get it to wrap within the column where it belongs, which is sometimes set to a fixed width to accomodate really complicated explanations Paragraph
$\nabla$ gradient operator Paragraph