(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Check whether the function [tex]f(x)=x^{-1/3}, 0<x<1,[/tex] belongs to the space

[tex]L^{2}(0,1)[/tex]

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

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

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

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# Homework Help: L2 Space check

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