# Definition:Absolutely Convergent Integral

## Definition

Let $I = \displaystyle \int_S f\left({x}\right) \, \mathrm d x$ be an improper integral, where $S$ is an unbounded closed interval.

$I$ is **absolutely convergent** if and only if $\displaystyle \int_S \left \vert {f \left({x}\right)}\right\vert \, \mathrm d x$ converges.