# Proving a Function Is Riemann Integrable

1. Mar 25, 2015

### Bashyboy

1. The problem statement, all variables and given/known data
Here is a link to the problem which I am currently working on:

2. Relevant equations

3. The attempt at a solution

The specific problem I am working on is found on page 3, and is the first problem on that page. The step I am having trouble with is

$$= \sum_{i=0}^{n-1} (x_{i+1} - x_i)(x^2_{i+1} + x_{i+1}x_i + x_i^2) (x_{i+1} - x_i)$$

$$< \delta 3 \sum_{i=0}^{n-1} (x_{i+1} - x_i)$$

What is going on?

Last edited by a moderator: May 7, 2017
2. Mar 25, 2015

### Dick

The point is that $x_i \le 1$ and $(x_{i+1}-x_i) \lt \delta$ for all $i$. Try using those inequalities.

Last edited by a moderator: May 7, 2017