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

[ss_1985]

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

 

[HallsofIvy]

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.

 

[ss_1985]

Can you give me a hint?