Is f(x)=x^(-1/3) in L2(0,1)?

[iamalexalright]

Homework Statement

Check whether the function $$f(x)=x^{-1/3}, 0<x<1,$$ belongs to the space
$$L^{2}(0,1)$$

Homework 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:

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?

 

[iamalexalright]

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

 

[lanedance]

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

 

[Dick]

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

Correct.

 

[iamalexalright]

Great, thanks!