My teacher mentioned this was a very important thing to know in calculus, he didn't explain too much about it but tried to emphasize how important is it.(adsbygoogle = window.adsbygoogle || []).push({});

If $$P=\{a,x,...,x_{k-1},x_{k},...,x_{n}=b\} , P^*=\{a,x,...,x_{k-1},x^*_{k},x_{k},...,x_{n}=b\}$$

Then, $$L_{f}(P)≤L_{f}(P^*)≤U_{f}(P^*)≤U_{f}(P) $$

"So adding pts to partition to get P* raises lower sum & decreases upper sum"

Any ideas guys?

Thanks

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# Calculus theorem/proof my teacher posted -- Not sure what it is...

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