- #1
steven187
- 176
- 0
hello all
Iv been working on a lot of integrability questions and I am having trouble with this problem
let f be integrable on [a,b] then show that |f| is integrable and that
[tex]|\int_{a}^{b}f|\le \int_{a}^{b}|f|[/tex]
now this is what i know
[tex]\int_{a}^{b^U}f =\int_{a_{L}}^{b}f= \int_{a}^{b}f[/tex]
[tex] U(f,P)-L(f,P)<\epsilon[/tex]
and
[tex]|f(x)|\le M \forall x\epsilon [a,b][/tex] is there anything else i can gain from a function being integrable on a closed interval?
muchly appreciated if someone could tell me where to start and some directions? I realize that it is only through practice that i will be able to know where to start and where to go from there, please help
thank you
steven
Iv been working on a lot of integrability questions and I am having trouble with this problem
let f be integrable on [a,b] then show that |f| is integrable and that
[tex]|\int_{a}^{b}f|\le \int_{a}^{b}|f|[/tex]
now this is what i know
[tex]\int_{a}^{b^U}f =\int_{a_{L}}^{b}f= \int_{a}^{b}f[/tex]
[tex] U(f,P)-L(f,P)<\epsilon[/tex]
and
[tex]|f(x)|\le M \forall x\epsilon [a,b][/tex] is there anything else i can gain from a function being integrable on a closed interval?
muchly appreciated if someone could tell me where to start and some directions? I realize that it is only through practice that i will be able to know where to start and where to go from there, please help
thank you
steven