One simple way: the set of discontinuity points of is . Taking into account that has not measure zero, is no Riemann integrable (as a consequence of a well known theorem).
3)b)
there is f(x) a continues and positive in [0,1]
g(x)=f(x) for rational x
g(x)=-f(x) for irational x
prove that g(x) is not integrabile in [0,1]
?
how i tried to solve it:
suppose that this not true and it integrabile
so so every dividing p
inf{S(p)-s(p)}=0
or i need to prove that infE=supT
now i need to get expresstion and prove that the equations above cannot exist.
what to do here in general
?