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Iv been working on alot of integrability questions and im 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 realise 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

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# Absolute value & integrability

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