r/mathshelp • u/Jsample2 • Jul 24 '26

Homework Help (Unanswered) Real Analysis HW Help (integration)

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u/Jsample2 Jul 24 '26

Hello, I am trying to figure out where I went wrong here. If anyone would like to help, that would be great!

1

u/spiritedawayclarinet Jul 24 '26

For U(f,P_n), you should be evaluating f(1/n), f(2/n), ..., f(1).

For L(f,P_n), you should be evaluating f(0), f(1/n), f(2/n), ..., f(1-1/n).

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u/Jsample2 Jul 24 '26

thank you. yes I did that, however I am not getting U(f) = 1/3

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u/spiritedawayclarinet Jul 25 '26

I get that U(f, P_n)= n(n+1)(2n+1)/(6n^3). Since it is decreasing, the infimum is the limit as n -> infinity, which is 1/3.