Im having some trouble with these ones

Decide if the following integrals exist as Lebesgue integrals and as Riemann integrals

$\displaystyle \int_{1}^{+ \infty} \frac{dx}{x^2}$

$\displaystyle \int_{0}^{+ \infty} \frac{sen^2(x)dx}{x^2}$

Thanks!!!

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- Jul 1st 2012, 10:59 AMkezmanRiemann Lebesgue integrals
Im having some trouble with these ones

Decide if the following integrals exist as Lebesgue integrals and as Riemann integrals

$\displaystyle \int_{1}^{+ \infty} \frac{dx}{x^2}$

$\displaystyle \int_{0}^{+ \infty} \frac{sen^2(x)dx}{x^2}$

Thanks!!! - Jul 1st 2012, 11:53 AMPlatoRe: Riemann Lebesgue integrals
- Jul 2nd 2012, 06:59 AMkezmanRe: Riemann Lebesgue integrals
As for riemann integral the first one exist and is = -1

The second one doesnt exist.

The problem is to prove if exists the lebesgue integral, I have no clue.:( - Jul 2nd 2012, 07:25 AMPlatoRe: Riemann Lebesgue integrals
- Jul 2nd 2012, 11:05 AMkezmanRe: Riemann Lebesgue integrals
ok the second integral if exists must be between 0 and 1

- Jul 2nd 2012, 12:01 PMPlatoRe: Riemann Lebesgue integrals
- Jul 2nd 2012, 01:00 PMkezmanRe: Riemann Lebesgue integrals
Excelent, so Ill have to fight against lebesgue integral.