1
$\begingroup$

I need some help here, folks...

Problem: If $f$ and $g$ are integrable on $[a,b]$ and $g(x) \leq f(x)$ for all $x \in [a,b]$, then $\int_a^b g \leq \int_a^b f$.

Any help would be great! Thanks!

  • 3
    Do you know a theorem that says something along the lines of, if $h$ integrable and $h\geq 0$, then $\int h \geq 0$?2012-11-28
  • 0
    Is this a Riemann integral question or Lebesgue?2012-11-28
  • 0
    If not, use the definition of (I'm assuming) Riemann integration, showing that the upper bound on any interval within a partition of $f$ is greater than $g$...2012-11-28

2 Answers 2