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

$\displaystyle S(p)=\sum_{i=1}^{n}M_{i}(x_{i}-x_{i-1)}$

$\displaystyle s(p)=\sum_{i=1}^{n}m_{i}(x_{i}-x_{i-1)}$

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

?