Consider the function $f(x)=x^3$. Prove it is Riemann integrable on $[0,1]$ using partitions.
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I would like to see it for this specific example. – theoxoxo Dec 09 '20 at 02:17
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It reduces to $\lim_{n\to \infty} \frac{1}{n} \sum_{k=1}^n \left(\frac{k}{n}\right)^3 = \frac{1}{n^4}\sum_{k=1}^n k^3$ and that last sum has a nice closed form. – RRL Dec 09 '20 at 02:29