Homework Help: Riemann integrability

1. Dec 18, 2017

Silviu

1. The problem statement, all variables and given/known data
Find a such that f is Riemann integrable on [0,1], where:
$f = x^acos(1/x)$, x>0 and f(0) = 0

2. Relevant equations

3. The attempt at a solution
I found at previous points a such that f is continuous, bounded and derivable, but I am not sure how to use that (as all these implications work just one way). Also the definition with partitions seems hard to use here. Any hint?

Last edited by a moderator: Dec 19, 2017
2. Dec 19, 2017

Staff: Mentor

You should have a statement "a function is Riemann integrable if it is [...]" that helps with all a where it is integrable. For the rest you'll have to see how to show that it is not.