Can you give me an example of function $f$'s improper integral converges but $f\cdot f$'s integral doesn't converge?

Asked Sep 19 '23 at 02:54

Active Sep 19 '23 at 21:43

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Could you provide me with an example: a function $f$ is a positive continuous function, and the integral of $f$ from $a$ to positive infinity converges, but the integral of the square of $f$ from a to positive infinity does not converge.

edited Sep 19 '23 at 03:05

Ricky

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asked Sep 19 '23 at 02:54

Leo Wang

3

$x^{- {1 \over 2}}$. – copper.hat Sep 19 '23 at 03:00

Can you give me an example of function $f$'s improper integral converges but $f\cdot f$'s integral doesn't converge?

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