anonymous
  • anonymous
Let f be a continuous and bounded function on [a,b] such that if
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
any idea?
anonymous
  • anonymous
not really,but it kind of looks like a set up for integrating by parts

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anonymous
  • anonymous
I guess so..
anonymous
  • anonymous
F'(x)=f(x) so we can say F'(t)=f(t) right..
anonymous
  • anonymous
that is what i was thinking, yes
anonymous
  • anonymous
maybe not exactly what you want, but you would get something like \(gF-\int f g'\)
anonymous
  • anonymous
\[\lim_{b \rightarrow} \int\limits_{0}^{b }G(t)F'(t)dt=\]
anonymous
  • anonymous
I guess enough to show that \[\int\limits f g'\] is convergent
anonymous
  • anonymous
first part is no problem, since \(\lim_{t\to \infty}g(t)=0\) and \(\int_a^\infty f(t)\) is bounded
anonymous
  • anonymous
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
  • anonymous
because all you know about \(g'\) is that \(g'\leq 0\)
anonymous
  • anonymous
does this come in a section after some theorem or lemma that maybe you are supposed to use?
anonymous
  • anonymous
no, this is homework, but prof gave the hint and said that you should use integration by part..
anonymous
  • anonymous
well then i guess this is the right approach!
anonymous
  • anonymous
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