Hello,
For one of the integration questions I have to do, I need to show that
is Lebesgue integrable, where 1 is the indicator function, and that
.
Does anyone have any ideas about how I would solve this? Thanks for any help!
Hello,
For one of the integration questions I have to do, I need to show that
is Lebesgue integrable, where 1 is the indicator function, and that
.
Does anyone have any ideas about how I would solve this? Thanks for any help!
To see that is Lebesgue-integrable, show that is dominated by some multiple of . (Notice that is bounded as .)
To calculate the integral, let . Differentiate twice under the integral sign to see that . You can evaluate that integral (integration by parts twice) to get . Then integrate twice, using the fact that to get the constants of integration, and you will find that .