# Decreasing function integral

• November 2nd 2012, 03:39 PM
Cesc1
Decreasing function integral
Hi, everybody! I'm just taking my first integral calculus course, so I'm having a little trouble with some things. I hope you can guide me to prove this:

"If f is a decreasing function on [a, b], prove that f is integrable."

Thanks!
• November 2nd 2012, 03:53 PM
Plato
Re: Decreasing function integral
Quote:

Originally Posted by Cesc1
"If f is a decreasing function on [a, b], prove that f is integrable."

A decreasing function on $[a,b]$ then the set of discontinuities is countable.
That means the function is Riemann integrable.