# Homework Help: Limit of integrable functions

1. Dec 11, 2008

### tomboi03

Prove: If f is integrable on [a , b] then
lim f =0
x$$\rightarrow$$a+

the integral goes from a to x.

How do i go about and prove this? I'm confused.
Thank You

Last edited: Dec 11, 2008
2. Dec 11, 2008

### HallsofIvy

Re: integrable?

Do you mean
$$\lim_{x\rightarrow a^+} \int_a^x f(t)dt= 0$$

The way you have written it, that the limit of f is 0, makes no sense- that certainly is not necessarily true.

My suggestion here is the same as to your other question: use the definition of integral in terms of Riemann sums.

3. Dec 15, 2008

### tomboi03

Re: integrable?

I've never learn Riemann sum definition.
What is that?

4. Dec 15, 2008

### HallsofIvy

Re: integrable?

First, is what I wrote what you mean. And if you have never learned Riemann sums, what definition of $\int_a^b f(x)dx$ are you using?