Integrable Function

[suan123]

Give an example of a function \f : \mathbb{R} \rightarrow \mathbb{R} , such that \f is integrable but \f^2 is not integrable. Prove your result.

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[nooonuii]

ข้อความเดิมเขียนโดยคุณ suan123

Give an example of a function $f : \mathbb{R} \rightarrow \mathbb{R}$ , such that $f$ is integrable but $f^2$ is not integrable. Prove your result.

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$f(x)=\dfrac{1}{\sqrt{x}}\cdot \chi_{(0,1]}(x)$