Thread: Prove x^2 is integrable

1. Prove x^2 is integrable

Here is the question I'm working on:

Prove directly from the definition of integrability that $\displaystyle x^2$ is integrable on any $\displaystyle [a,b] \subset [0,\infty).$

I have just begun integrability, and am not so familiar with using the definition. I've set up the preliminaries, but do not know how to proceed. Any advice?

~Thanks.

2. Originally Posted by Anonymous1
Here is the question I'm working on:

Prove directly from the definition of integrability that $\displaystyle x^2$ is integrable on any $\displaystyle [a,b] \subset [0,\infty).$

I have just begun integrability, and am not so familiar with using the definition. I've set up the preliminaries, but do not know how to proceed. Any advice?

~Thanks.
You are talking about this from a Riemann-Stieltjes integrable persepctive, correct?

3. Yes I was, but I actually found a solution, i.e., proving integrability for some arbitrary, but small mesh. The meat of it was cracked via MVT, and using mass cancelation of the resulting telescoping series.