Find out a function R--> R such that it is integrable

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The discussion focuses on finding a function f: R → R that is integrable while its square f^2 is not integrable. The suggested function f(x) = 1/√x is deemed incorrect because its integral over the entire real line does not exist. Participants seek clarification and hints for identifying a suitable function that meets the criteria. The conversation emphasizes the need for the function to be defined over a specific interval to ensure integrability. Ultimately, the goal is to identify a valid example of such a function.
ss_1985
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Hi

The question asks to find out a function R--> R such that it is integrable, and its square is not.
Is f(x)=1/root x right?
The problem I thought was its only over an interval

Please help
thanks
 
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ss_1985 said:
Hi

The question asks to find out a function R--> R such that it is integrable, and its square is not.
Is f(x)=1/root x right?
The problem I thought was its only over an interval

Please help
thanks
No, 1/\sqrt{x} is not correct because
\int_{-\infty}^{\infty}\frac{dx}{\sqrt{x}}
does not exist.
 


Can you give me a hint?
 

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