Answer to Question #103843 in Real Analysis for BIVEK SAH

Question

The function f defined by f(x)= [x −1 ]where [x] is the greatest integer
function is integrable on the interval [2,4].


True or false

Answer 1

It is true. $f$ is continuous in $[2,4]$ almost everywhere (it is not continuous in $\{3,4\}$, and $\{3,4\}$ no more than countable set). By the Lebesgue's criterion for Riemann integrability $f$ is integrable on $[2,4]$.

Answer: true