i need some help with this proof. Please do not give me the solution i want to figure this on my own. ALl i need is your hints and steering.(adsbygoogle = window.adsbygoogle || []).push({});

Also note that i am on a first year level intro to real analysis course. I do however know the upper and lower reimann sums which is probably how this problem is to be solved.

Suppose f is continuous and non negative on [a,b]. Suppose f(c) > 0 for some c in (a,b). Prove that [tex] \int_{a}^{b} f > 0 . [/tex]

What worries me here is that f(c) does not include f(a) and f(b) exclusively. however how would i go about proving that? Would i have to use limits to show that for some epsilon [tex] \lim_{\epsilon \rightarrow 0} f(x - \epsilon) > 0 [/tex] and the same would apply for the f(b) paart??

I know that if i picked a partition P = {a,a+E,b-E,b} i would encounter this problem because of the explicit value (limit rather) of function at a nad b not being greater than zero.

P.S. i can't find a website that shows how to prove limits formally (although i have learnt it in the past i cannot find it in my notes).

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Help with a proof

**Physics Forums | Science Articles, Homework Help, Discussion**