Is there a function f: R->R is integrable but f^2 is not? why?

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- Aug 16th 2011, 02:03 PMparkloversquare of a function is not integrable
Is there a function f: R->R is integrable but f^2 is not? why?

- Aug 16th 2011, 02:17 PMPlatoRe: square of a function is not integrable
Theorem: If is an integrable function in then is an integrable function in .

P.S. In response to the to reply #3.

It depends on how one defines integral.

Most often Riemann integrals require bounded functions.

That example is not a bounced function.

The term is*improper integral.* - Aug 16th 2011, 02:32 PMgirdavRe: square of a function is not integrable
Consider and choose any value you want for .

- Aug 16th 2011, 02:51 PMparkloverRe: square of a function is not integrable
- Aug 16th 2011, 02:59 PMgirdavRe: square of a function is not integrable
The function is integrable but not its square. As you noticed, a primitive of is , but if you compute , you will find , and it has an infinite limit as .

- Aug 16th 2011, 03:00 PMPlatoRe: square of a function is not integrable