Determine whether the function f: [0,1] R given by:
1 if \
is Riemann integrable on [0,1].
I know that if it is Riemann integrable, sup L(P, f) = inf U(P,f), P being the partition of [0,1]
or (lower integral of f over [0,1]) = (upper integral of f over [0,1])
How do I show if it is or not?
so does that mean it's not Riemann integrable because the sup doesn't equal the inf?
You tell me. And justify your answer. (I will verify it if you do)
Originally Posted by thaopanda
so L(P,f) = where = inf f(x)
and U(P,f) = where = sup f(x)
since sup f = 3 and inf f = 1,
and because that's the maximum partition in [0,1]
sup L(P,f) 1
inf U(P,f) 3
but the sup f = 3... yeah, I'm lost... (Crying)