Finding Riemann Integrability for f(x) on [0,1]

[Silviu]

Homework Statement

Find a such that f is Riemann integrable on [0,1], where:
$f = x^acos(1/x)$, x>0 and f(0) = 0

Homework Equations

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?

 

[mfb]

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).

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.