3)b)

there is a continues and positive f in [0,1]

prove that g(x) is not integrabile in [0,1]

g(x)=f(x) for rational x

g(x)=-f(x) for irational x

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

why its not integrible?

because f the endless points of disconinuety?

my prof showed a function

g(x)=1 for rational x

g(x)=1/x for irational x

and he said that it is integrible

i dont know why the original is not integrible

?