Define the set E ={ 1/n : n is a natural #} contained in [0,1]. Prove that the function
f(x) = {1, when x exists in E
0, otherwise}
is Riemann integrable on [0,1]. What is the value of the integral of f(x)dx from 0 to 1

Question

Define the set E ={ 1/n : n is a natural #} contained in [0,1]. Prove that the function 
f(x) = {1, when x exists in E
            0, otherwise}
is Riemann integrable on [0,1]. What is the value of    the integral of f(x)dx from 0 to 1

anonymous · Answer

the integral is zero for sure, as the function is zero almost everywhere (all but a countable set of point) but that is not a proof, just a statement.

anonymous · Answer

i know that the U(f,P) = L(f,P)  in order for it to be integrable, but I just started this class and don't understand how to solve for those sums.