Question

I have a continuous function f for all x in R satisfied \[\int_{-\infty}^{x} {f(u)du}\]\ for all x in R.
\[\f>0\]\ for all x in R?

Answer 1

What is your question exactly??

Answer 2

let me get this straight...\[f:\forall x\in\mathbb R\]we have\[\int_{-\infty}^{x}f(u)du\]and you want to know if that means \[f>0:\forall x\in\mathbb R\]?

Answer 3

my question : \[\forall x \in \mathbb{R}, f>0\]. True or false?

Answer 4

are you told any more info, like that the integral converges or something?

Answer 5

Sorry, the above integral >0 \[\forall x \in \mathbb{R}\]

Answer 6

so we have the full question as:
for\[f:\forall x\in\mathbb R\]we have\[\int_{-\infty}^{x}f(u)du>0\]does this mean that \[\forall x\in\mathbb R,~f>0\]?

Answer 7

Additionally,f is continuous. Does \[f>0, \forall x \in \mathbb{R}\]?

Answer 8

bookmark

Answer 9

\(f\) does not have to be positive for all values of \(x\)

Answer 10

Can you give me an example?

Answer 11

Can we take the derivative of this inequality with respect to x: \[ \frac{d}{dx} (\int_{-\infty}^{x} f(u)du) > \frac{d}{dx}(0) \]? Or is it unnecessary?

Answer 12

\[\int_{\infty}^x(\sin(x)+\frac{1}{2})dx\] could do it

Answer 13

that integral does not converge for ant value of x

Answer 14

*any

Answer 15

oh no it won't do it since it wont

Answer 16

what zarkon said

Answer 17

try making a function f that looks like this...