Homework Help: L2 Space check

1. Aug 31, 2010

iamalexalright

1. The problem statement, all variables and given/known data
Check whether the function $$f(x)=x^{-1/3}, 0<x<1,$$ belongs to the space
$$L^{2}(0,1)$$

2. Relevant equations
Well, I missed this lecture so not really sure how to go about this but from what I gathered:

A function is in L2 if the function is square integrable

If that is the case then:

3. The attempt at a solution

$$\int^{1}_{0}(x^{-1/3})^{2}dx = \int^{1}_{0}(x^{-2/3})dx = 3x^{1/3}|^{1}_{0} = 3$$

Since the solution exists then the function is in L2, correct?

2. Aug 31, 2010

iamalexalright

if that method is correct then it would not exist in L2(0,infinity), correct?

3. Aug 31, 2010

lanedance

that all sounds reasonable to me, though i'm not an expert in these things

4. Aug 31, 2010

Dick

Correct.

5. Aug 31, 2010

iamalexalright

Great, thanks!