Improper integral/Continuous unbounded positive function/Improper integral exists/Example/Exercise

Give an example of a not bounded, continuous function

$f\colon \mathbb {R} _{\geq 0}\longrightarrow \mathbb {R} _{\geq 0},$

such that the improper integral ${}\int _{0}^{\infty }f(t)dt$ exists.

Create a solution