Question

Let \(f:[0,1]\rightarrow \mathbb R\) \(f(x) =1 if x =1/n\), n an integer, and f(x) =0 otherwise.
a) Prove that f is integrable
b) Show that \(\int _0^1 f(x) dx =0\)

Answer 1

I think that we have to apply the theorem of implicit functions

Answer 2

I'm referring to the general cse, namely m dependent variables, and n independent variables

Answer 3

case*

Answer 4

Please, can you post the previous exercise, so, using the theorem of implicit functions, I will show you why we have to get a 4x4 matrix @Loser66

Answer 5

My prof wants me show
\(\forall \varepsilon ~~~~\exists \) a partition \(P_\varepsilon\) such that
\(U(f, P_\varepsilon)-L(f, P_\varepsilon)< \varepsilon\)

Answer 6

@Michele_Laino . that is not my problem, for some reasons, I posted the wrong one.

Answer 7

ok! thanks anyway! @Loser66

Answer 8

I am given a special partition: P ={0,1/n, (1/n)+(1/n^2), (1/n)+(2/n^2),.......1}