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In trying to solve Riemann Integrals by definition, I cant understand certain things.

For example, if you take this post : How to evaluate this Riemann integral using this definition? , the two answers take the limit (n to infinite) of the Upper and Lower sums in the partition proposed, and if the limits are equal, then the function is Riemann Integrable.

What is the logic behind that? Why take the limit? Sorry if the question is too silly but I cant find anywhere an explicit explanation of this.

Thanks!

UDAC
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  • The question that you have mentioned contains the answer to that question. – José Carlos Santos Dec 20 '21 at 09:02
  • @JoséCarlosSantos I simply dont understand the logic of taking the limit n to infinite of the Upper and LowercSums – UDAC Dec 20 '21 at 09:05
  • @JoséCarlosSantos This post answer my question ? https://math.stackexchange.com/questions/2045722/why-is-the-upper-riemann-integral-the-infimum-of-all-upper-sums/2047959#2047959 – UDAC Dec 20 '21 at 09:11

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