cinar
Let f be a continuous and bounded function on [a,b] such that if



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cinar
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cinar
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any idea?

anonymous
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not really,but it kind of looks like a set up for integrating by parts

cinar
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I guess so..

cinar
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F'(x)=f(x)
so we can say F'(t)=f(t) right..

anonymous
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that is what i was thinking, yes

anonymous
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maybe not exactly what you want, but you would get something like \(gF\int f g'\)

cinar
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\[\lim_{b \rightarrow} \int\limits_{0}^{b }G(t)F'(t)dt=\]

cinar
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I guess enough to show that \[\int\limits f g'\] is convergent

anonymous
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first part is no problem, since \(\lim_{t\to \infty}g(t)=0\) and \(\int_a^\infty f(t)\) is bounded

anonymous
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yeah you hit the nail on the head, and frankly i don't see why that is true, so this might be the wrong approach

anonymous
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because all you know about \(g'\) is that \(g'\leq 0\)

anonymous
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does this come in a section after some theorem or lemma that maybe you are supposed to use?

cinar
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no, this is homework, but prof gave the hint and said that you should use integration by part..

anonymous
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well then i guess this is the right approach!

cinar
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